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Handoff Management and Admission Control Using Virtual Partitioning With Preemption in 3G Cellular/802.16e Interworking Enrique Stevens-Navarro, Member, IEEE, Vahid Shah-Mansouri, Student Member, IEEE, and Vincent W. S. Wong, Senior Member, IEEE
Abstract—The integration of third-generation (3G) cellular networks and IEEE 802.16e networks is an important interworking case within the forthcoming fourth-generation heterogeneous wireless networks. In this paper, we extend the virtual partitioning with preemption technique for admission control in cellular/802.16e interworking and evaluate its performance. First, we describe the mobility scenario between 3G cellular networks and IEEE 802.16e networks in terms of the horizontal (intrasystem) and vertical (intersystem) handoffs that can occur and derive the corresponding handoff rate equations. We then propose admission-control algorithms for connection requests that consider the class of service (i.e., real time or nonreal time) and the type of user (i.e., new or handoff). For the handoff requests, a different priority is assigned to each type of handoff. A joint connection- and packet-level optimization approach is used for quality-of-service (QoS) provisioning. The accuracy of the analytical model is validated via simulations. Numerical results show significant performance improvement. The blocking probabilities for new connection requests can be reduced by 70% when the joint QoS optimization approach is used. Index Terms—Admission control, cellular/802.16e interworking, handoff management, heterogeneous wireless networks.
I. I NTRODUCTION
A
BROAD range of wireless access technologies is being deployed worldwide. Examples include the thirdgeneration (3G) cellular systems such as the Universal Mobile Telecommunications System and CDMA2000, wireless local area networks (WLANs), and broadband wireless systems such as Worldwide Interoperability for Microwave Access (WiMAX). The integration of all these networks is usually called the fourth-generation (4G) heterogeneous wireless networks [1]. The IEEE 802.16e standard (also called mobile WiMAX) [2] includes the support for mobile terminals. Ben-
Manuscript received July 16, 2008; revised January 19, 2009, May 1, 2009, and July 17, 2009. First published September 15, 2009; current version published January 20, 2010. This work was supported in part by Bell Canada, by the Natural Sciences and Engineering Research Council of Canada, and by the Programa de Mejoramiento del Profesorado from Mexico. The review of this paper was coordinated by Prof. Y.-B. Lin. E. Stevens-Navarro is with the Faculty of Science, Universidad Autonoma de San Luis Potosi, 78290 San Luis Potosi, Mexico (e-mail:
[email protected]). V. Shah-Mansouri and V. W. S. Wong are with the Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail:
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2009.2032235
efits such as complementary coverage, lower deployment cost, and quality-of-service (QoS) support make IEEE 802.16e an important candidate to complement existing 3G cellular networks. It is envisioned that WiMAX will be deployed in different phases. It is also crucial to fill the WiMAX coverage gaps with the existing 3G cellular systems to provide a ubiquitous and seamless user experience. Thus, within the 4G heterogeneous wireless networks, the interworking of 3G cellular systems with mobile WiMAX is a specific case that has recently gained a lot of attention from the research and standardization communities [3], [4]. Such integration can facilitate service providers to reuse some existing back-end systems. It can simplify network management and customer acquisition and converge the billing aspects. Since IEEE 802.16e is connection oriented, it can also support internet protocol (IP) multimedia services. Currently, standardization on the interworking architecture between 3G cellular networks and IEEE 802.16e networks is being conducted within the Network Working Group (NWG) of the WiMAX Forum [5]. The NWG is developing specifications for the architecture, protocols, and services for mobile 802.16e systems. A loosely coupled architecture for cellular/802.16e interworking with QoS support is proposed in [6]. An interworking architecture at the protocol and signaling level is proposed in [7] within the context of 3G cellular IP multimedia services. An architecture for integrating mobile WiMAX within the 3G wireless network is proposed in [8]. In cellular/802.16e interworking, due to mobility, users are able to switch connections among networks. This process is called handoff. A handoff is defined as horizontal if it occurs between two adjacent cells of the same system. On the other hand, it is defined as vertical if it occurs between two cells of different systems. Since there are now two types of handoffs, each one with different execution procedures (e.g., signaling overhead, context, and authentication transfer), the traditional approach of giving priority to horizontal handoff users over the new users needs to be extended. In fact, as the interworking architecture is fully deployed and the dual-mode terminals become available, the number of vertical handoffs will significantly increase. Thus, novel handoff-management techniques are required, and appropriate mobility scenarios should be investigated. The support for multiclass services (e.g., multimedia sessions) and the joint design at the connection and packet levels are important design objectives for admission control and
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QoS provisioning in 4G heterogeneous wireless networks [1]. Admission control is required to limit the number of connections that can be accepted into the network, whereas QoS provisioning guarantees that the resources are efficiently used and satisfy the application requirements. Admission control algorithms for multiservice fixed broadband wireless networks have been proposed in [9]–[11]. Admission control algorithms for IEEE 802.16e have recently been proposed in [12]–[14]. Previous works in [9]–[14] only consider IEEE 802.16 systems and do not consider the interworking of IEEE 802.16e systems with 3G cellular networks. Virtual partitioning (VP) is an efficient, fair, and robust resource-sharing technique. VP with the support for multiclass services is proposed in [15] for wireline networks. It works under the idea of preallocating a nominal capacity for each service. In [16], VP is considered for admission control in cellular networks. Two schemes with preemption considering real-time (RT) and non-RT (NRT) connections are presented. RT connections receive guaranteed access, whereas NRT connections can utilize any unused capacity. Following the joint call- and packet-level QoS optimization approach in [17] and [18], QoS constraints are considered at the call level in terms of the blocking/dropping probabilities and at the packet level in terms of the packet-loss probabilities. However, none of those previous works in [16]–[18] consider the heterogeneous wireless access networks and the interworking between 802.16e and 3G systems. In [19], we study the use of VP for admission control in an integrated cellular/WLAN system. By following the concept of policy functions introduced in [20] for admission control, the corresponding policy functions for VP are derived. However, only RT connections are considered for admission control, and preemption is not being used. In addition, only the connection level is considered in the optimization framework. In [21], VP is considered for resource sharing in cellular/WLAN systems. Resource management for multiclass services and load balancing are also investigated. However, mobility issues such as horizontal and vertical handoffs are not considered. In this paper, we propose the use of VP with preemption for admission control in cellular/802.16e interworking and evaluate its performance [22]. Our model formulation considers the joint design at the connection and packet levels. To this end, we first present the mobility scenario between 3G cellular networks and IEEE 802.16e networks. The mobility scenario specifies the horizontal and vertical handoffs that can occur in cellular/802.16e interworking. The corresponding set of handoff rate equations is derived. To the best of our knowledge, this is the first attempt to model this expected scenario. The contributions of our work are given in the list that follows. 1) We propose admission-control algorithms for different types of connection requests. For horizontal and vertical handoff users, different priorities are assigned to each user according to the mobility scenario. Preemption rules are defined for the RT and NRT connections when VP with preemption is used. 2) We derive the blocking and dropping probabilities at the connection level and the packet-loss probability at the packet level. We formulate a blocking/dropping cost
minimization problem following a joint connection- and packet-level QoS optimization approach. 3) The accuracy of the analytical model is validated via simulations. The performance of the integrated cellular/802.16e system using VP with preemption is evaluated. Numerical results show significant performance improvement. The blocking probabilities for new connection requests can be reduced by 70% when the joint QoS optimization approach is used. The rest of this paper is organized as follows: Section II presents the system model and mobility scenario for cellular/802.16e interworking. Section III describes the use of VP with preemption, the proposed admission algorithms, and the cost-minimization problem. Section IV presents the performance evaluation results. Conclusions are given in Section V. II. S YSTEM M ODEL Consider an integrated cellular/802.16e system, as shown in Fig. 1. A 3G cellular radio access network (RAN) is deployed covering all the service area. In a highly populated area or region with high service demand, an IEEE 802.16e access service network (ASN) is also deployed to provide an additional capacity. This will be a common deployment alternative [23]. As mentioned in Section I, the NWG is developing an endto-end network architecture for IEEE 802.16e networks. It considers the loosely coupled interworking architecture [5], in which the access networks are interconnected through the Internet by a gateway. Medium-access control (MAC) of the IEEE 802.16e ASN operates in the point-to-multipoint mode. Thus, the mobile terminals are served by a centralized base station. If the base stations of both systems are colocated [3], then we have an overlapped system. A. Mobility Scenario Referring to the integrated cellular/802.16e system in Fig. 1, horizontal handoffs can occur due to mobility of users among neighboring base stations of the same network (e.g., between two adjacent cells of the 3G RAN). The handoff decision is based on the received signal strength. On the other hand, vertical handoffs can occur in two cases: First, it can happen when a user leaves a cell, and the mobile terminal can select another network to obtain services. The handoff decision may incorporate other factors such as monetary cost, types of QoS guarantees, and user’s preferences [24], [25]. In this case, the vertical handoff is optional because, although it is not required, it may improve the QoS of the connection. A vertical handoff can also occur when a horizontal handoff cannot successfully be completed in the overlapped coverage area. Here, the handoff request is vertically transferred to the other network to avoid the connection from being dropped. We consider both types of vertical handoff in our mobility model. B. Traffic and Mobility Models We first introduce the notations. Let Mc and Me denote the sets of cells in the 3G RAN and the 802.16e ASN, respectively.
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STEVENS-NAVARRO et al.: HANDOFF MANAGEMENT AND ADMISSION CONTROL USING VP WITH PREEMPTION
Fig. 1.
433
Integrated 3G cellular/802.16e system.
Fig. 2. Integrated 3G cellular/802.16e system, 3G RAN with |Mc | = 12, and 802.16e ASN with |Me | = 3.
For each cell i ∈ Mc , let Aci denote the set of 3G cells adjacent to cell i. For each cell k ∈ Me , let Aek denote the set of 802.16e cells adjacent to cell k. Let Wic denote the set of overlapping 802.16e cells to cell i ∈ Mc . Let Wke denote the set of overlapping 3G cells to cell k ∈ Me . As an example, Fig. 2 shows an integrated cellular/802.16e system with Mc = {C1, C2, C3, . . . , C11, C12} and Me = {E1, E2, E3}. Thus, we have AcC2 = {C1, C3, C4, C5, C6, C7}, e c e = {C2}. AE2 = {E1, E3}, WC2 = {E2}, and WE2 In the 3G RAN, when a connection is established, a circuit bearer service is created. It has several QoS attributes that describe how the packets in that service class should be treated. The Third-Generation Partnership Project (3GPP) defined four different classes of QoS for connections [26]: conversational, streaming, interactive, and background. In the 802.16e ASN, when a connection is established, a service flow is created in the MAC layer with specific QoS parameters. The IEEE 802.16e defined five different classes of QoS for service flows [2]: unsolicited grant service (UGS), real-time polling service (rt-PS), extended rt-PS (Ert-PS), nonreal-time polling service
(nrt-PS), and best effort (BE). For admission control, conversational, streaming, UGS, rt-PS, and Ert-PS classes are grouped into RT connections, whereas interactive, background, nrt-PS, and BE classes are grouped into NRT connections. Let S denote the set of services available to the mobile users. The services are classified into two groups: RT services as SRT and NRT services as SNRT . Thus, SRT ⊂ S and SNRT ⊂ S. A service s ∈ S requires bcs basic bandwidth units (BBUs) and bes BBUs to guarantee its QoS requirements in the 3G RAN and the 802.16e ASN, respectively. For i ∈ Mc , k ∈ Me , and s ∈ S, the new connection requests for service s arrive at cells i and k according to independent Poisson processes with rates λcis and λeks , respectively. The connection duration of service s, i.e., ts , is exponentially distributed with mean 1/vs . Since the exponential distribution is memoryless, the residual (i.e., remaining) connection time tR s is also exponentially distributed with mean 1/vs . For i ∈ Mc and k ∈ Me , we assume that the cell residence times tci and tek are also exponentially distributed with means 1/ηic and 1/ηke , respectively. The channel holding time in cell i is defined as the time that a user continues to use the assigned bcs BBUs in the 3G RAN (i.e., a circuit bearer service), whereas in cell k, it is the time that a user continues to use the assigned bes BBUs in the 802.16e ASN (i.e., a service flow in the MAC layer). For service s ∈ S, the channel-holding time in cells i and k are obtained as c R e R c e min(tR s , ti ) and min(ts , tk ), respectively. Since ts , ti , and tk c are exponentially distributed for all s ∈ S, i ∈ M , and k ∈ Me , the holding times are also exponentially distributed with parameters μcis = vs + ηic and μeks = vs + ηke , respectively. A user of service s in cell i ∈ Mc may terminate its connection at the end of its channel-holding time and leave the integrated system with probability qics = υs /(υs + ηic ). Otherwise, it may move within the system and continue in an adjacent cell with probability 1 − qics . We have cc qij + qilces (1) 1 − qics = s j∈Aci
l∈Aek , k∈Wic
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cc where qij denotes the probability of attempting a horizontal s handoff from cell i ∈ Mc to a neighboring cell j ∈ Aci , and qilces denotes the probability of attempting a vertical handoff from cell i to a neighboring cell l ∈ Aek of an overlapped cell k ∈ Wic . Similarly, a user of service s in cell k ∈ Me may terminate its connection at the end of its channel holding time and leave the integrated system with probability qkes = υs /(υs + ηke ). Otherwise, it may move within the system and continue in an adjacent cell with probability 1 − qkes . We have
1 − qkes =
ee qkl + s
j∈Aci ,
l∈Aek
ec qkj s
(2)
i∈Wke
ee where qkl denotes the probability of attempting a horizontal s handoff from cell k ∈ Me to a neighboring cell l ∈ Aek , and ec denotes the probability of attempting a vertical handoff qkj s from cell k to a neighboring cell j ∈ Aci of an overlapped cell i ∈ Wke . The arrival rates of service s to cells i and k, i.e., φcis and e φks , respectively, include all the connection requests from the new, horizontal, and vertical handoff users. They are given by
φcis = λcis +
ec hcc jis + Ψis
∀ i ∈ Mc
ce hee lks + Ψks
∀ k ∈ Me
who leave the neighboring cell l. We can state the handoff rate equations as follows: c c cc c cc hcc hcc jis = λjs 1 − Bnjs qjis + xjs 1 − Dhhjs qjis
+
ec vki + s
k∈Wic
Ψce ks =
i∈Wke
(7)
ec ec e ec = λeks 1 − Bne ks qkj + hee vkj xks 1 − Dhhks qkjs s s
+
x∈Aek
ce e ec vyk 1 − D vhks qkjs s
y∈Acz ,z∈Wke
+
ce e ec vzk 1 − Dvh qkj s ks
(8)
z∈Wke
e e ee ee e ee 1 − B q 1 − D hee = λ + h lks ls nls lks xls hhls qlks
+ +
(4)
x∈Ael
ce e ee 1 − Dvh qlk vyl s s ls
ce e ee 1 − Dvh qlk vzl s ls
(9)
z∈Wle
ec vli s
∀ i ∈ Mc
(5)
l∈Aek , k∈Wic ce vik + s
ec c cc 1 − Dvh qji vzj js s
y∈Acz ,z∈Wle
where hcc jis denotes the horizontal handoff rate of service s offered to cell i from its adjacent cell j ∈ Aci , and hee lks denotes the horizontal handoff rate of service s offered to cell k from its adjacent cell l ∈ Aek . On the other hand, the terms Ψec is and denote the vertical handoff rates offered to cells i and k, Ψce ks respectively. From the described mobility scenario, the vertical handoff rates in (3) and (4) are given by
z∈Wjc
(3)
l∈Aek
Ψec is =
ec c cc 1 − D vyj vhjs qjis s
y∈Aez ,z∈Wjc
j∈Aci
φeks = λeks +
+
x∈Acj
ce vjk s
ce ce c ce vjk = λcjs 1 − Bnc js qjk + hcc xjs 1 − Dhhjs qjks s s
+
ec c ce 1 − D vyj vhjs qjks s
y∈Acz ,z∈Wjc
+
ec c ce 1 − Dvh qjk vzj js s
z∈Wjc
ec = vki s
e hee xks Dhhks +
x∈Aek
∀ k ∈ Me
(6)
j∈Aci , i∈Wke
ec denotes the vertical handoff rate of service s offered where vki s ec denotes the to cell i from its overlapped cell k ∈ Wic , vli s vertical handoff rate of service s offered to cell i from a ce neighboring cell l ∈ Aek of an overlapped cell k ∈ Wic , vik s denotes the vertical handoff rate of service s offered to cell k ce denotes the vertical from its overlapped cell i ∈ Wke , and vjk s handoff rate of service s offered to cell k from a neighboring cell j ∈ Aci of an overlapped cell i ∈ Wkc . The first term in both (5) and (6) corresponds to transferred vertical handoffs, whereas the last term corresponds to optional vertical handoffs. Note that, in (5), the transferred vertical handoff requests [i.e., the first term in the right-hand side in (5)] are issued by the overlapped cell k (not by the mobile users). On the other hand, the optional vertical handoff requests [i.e., the second term in the right-hand side in (5)] are issued by the mobile users
x∈Acj
ce = vik s
x∈Aci
ce e vyk Dvh s ks
(10) (11)
y∈Aci
c hcc xis Dhhis +
ec c vyi Dvh s is
(12)
y∈Aek
where Bnc is and Bne ks are the probabilities of blocking connection requests from new users of service s in cells i ∈ Mc and c e and Dhh are the probabilities k ∈ Me , respectively. Dhh is ks of dropping connection requests from horizontal handoff users c of service s in cells i ∈ Mc and k ∈ Me , respectively. Dvh is e and Dvhks are the probabilities of dropping connection requests from vertical handoff users of service s in cells i ∈ Mc and k ∈ Me , respectively. III. VP W ITH P REEMPTION FOR A DMISSION C ONTROL Each cell i ∈ Mc has a capacity of Cic BBUs. Recall from Section II that the transmission rate of service s in the 3G RAN (i.e., bcs ) is normalized with respect to the BBUs. Due to
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STEVENS-NAVARRO et al.: HANDOFF MANAGEMENT AND ADMISSION CONTROL USING VP WITH PREEMPTION
scheduling and statistical multiplexing, each cell i supports |S| different services and can admit connections with at most Nic BBUs, where Nic ≥ Cic . The value of Nic is a design parameter [16], [18]. If Nic has a small value, then the cell may experience a low packet-loss probability and a high connection blocking probability. On the other hand, if Nic has a large value, then the cell may experience a low connection blocking probability and a high packet-loss probability. This happens because Nic restricts the number of connections that can be admitted, and the capacity Cic restricts the number of transmitted packets from the admitted connections. Finally, if Nic = Cic , then there is no statistical multiplexing gain. According to the QoS classification mentioned in Section II, services are grouped into two types: RT and NRT. For admission control in cellular/802.16e interworking, by extending one of the resource allocation schemes proposed in [16], we can use VP with preemption for the NRT group. Thus, the RT group is offered guaranteed access, whereas the NRT group is offered best effort access. The basic idea of VP is as follows: In each cell i ∈ Mc , i.e., a nominal capacity or nominal allocation of c c and NNRT , is assigned to RT and NRT connections, NRT i i c c + NNRT = Nic . The resource respectively, such that NRT i i allocation in cell i of the 3G RAN is defined as mcis bcs ≤ Ngci ∀ i ∈ Mc ; g ∈ {RT, NRT} (13) s∈Sg
where mcis is the number of service s connections in cell i. Given the nominal allocations, VP defines a group as underloaded if all connections from that group are assigned fewer resources than its nominal allocation and as overloaded if all connections from that group are assigned more resources than its nominal allocation. In VP, the unused capacity in the underloaded RT group can be utilized by the NRT connections if necessary. The RT connections receive guaranteed access and better QoS. They can preempt the NRT connections when the NRT group is overloaded. VP can be considered as a generalization of complete sharing and complete partitioning of network resources among different classes. When the arrival rates from all classes are low, the behavior of VP is similar to complete sharing. On the other hand, when the arrival rates from all classes are high, VP behaves as complete partitioning. Similarly, each cell k ∈ Me has a capacity of Cke BBUs. Each cell k supports |S| different services and can admit connections with at most Nke BBUs, where Nke ≥ Cke . The e and parameter Nke of cell k ∈ Me is also partitioned into NRT k e e e e NNRTk , with NRTk + NNRTk = Nk . The resource allocation in cell k of the 802.16e ASN is defined as meks bes ≤ Ngek ∀ k ∈ Me ; g ∈ {RT, NRT} (14) s∈Sg
where meks is the number of service s connections in cell k. A. Admission Control for New Requests In addition to the priority of RT connections over NRT connections, for admission control, the mobility of the users also needs to be taken into account. In the case of cellular/802.16e
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interworking, we consider connection requests from new, horizontal, and vertical handoff users. To this end, we propose admission control algorithms for each type of connection request. The admission algorithm for the new requests using VP with preemption is shown in Algorithm 1. Algorithm 1—Admission control algorithm for new request with bandwidth requirement bcs in cell i ∈ Mc . 1: if s ∈ SRT c c c 2: if s ∈SNRT mis bs > NNRTi c c c 3: if s ∈S mis bs + bs ≤ Nic − δic , 4: then accept 5: else if ( s ∈S mcis bcs ≥ Nic − δic and c c c c c s ∈SRT mis bs + bs ≤ NRTi − δi ), 6: then accept with preemption 7: else reject c − δic , 8: else if s ∈SRT mcis bcs + bcs ≤ NRT i 9: then accept 10: else reject 11: if s ∈ SNRT , s ∈S mcis bcs + bcs ≤ Nic − δic , 12: then accept 13: else reject 14: end Let δic denote the number of BBUs that can be reserved for connection requests from the handoff users of any type in each c c nominal allocation (i.e., NRT and NNRT ) in cell i ∈ Mc . Consider the case for a connection request from service s ∈ SRT c in cell i ∈ Mc (see Algorithm 1, step 1). We have NRT − δic i BBUs that can be used for connection requests from either new, horizontal, or vertical handoff users. Whenthe NRT group is underloaded, the new request is accepted if s ∈SRT mcis bcs + c bcs ≤ NRT − δic (see Algorithm 1, step 8). On the other hand, i c if the NRT group is overloaded, s ∈SNRT mcis bcs > NNRT i (Algorithm 1, step 2), then two situations can happen. First, if the total amount of resources used bythe RT users, the c c overloaded part of the NRT users (i.e., s ∈SNRT mis bs − c c NNRTi ), and the new connection is less than or equal to NRTi − δic , then the connection is accepted (see Algorithm 1, steps 3 and 4). Otherwise, preemption is invoked, and some connections from the NRT group are removed. To achieve preemption, suitable rules need to be defined. These rules specify whether the preemption of RT connections over NRT connections can be applied based on the number of users of each service. We modified and extended the original preemption rules in [16] to consider connection requests from the vertical handoff users and to include our proposed admission-control algorithms. The preemption rules for the connection requests from the new users are defined as follows: Preemption happens when a connection request from a new user of service s ∈ SRT arrives under the conditions that the NRT group is overloaded, s ∈S mcis bcs ≥ Nic − δic , and c c c c c s ∈SRT mis bs + bs ≤ NRTi − δi (see Algorithm 1, steps 5 c and 6). Recall that new requests can only use NRT − δic BBUs. i Thus, new connection requests are accepted with preemption c until we reach the point where NRT − δic BBUs are used by i the connections of the RT group.
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For connection requests from service s ∈ SNRT in cell i ∈ Mc , a new request is accepted if s ∈S mcis bcs + bcs ≤ Nic − δic (see Algorithm 1, steps 11 and 12). Note that the parameter c to allow Nic is used instead of the nominal allocation NNRT i the connections from the NRT group to use all the available capacity in cell i. If preemption of a connection from service s ∈ SRT happens over services s ∈ SNRT , termination only applies to one service in SNRT , which is uniformly selected at random (i.e., 1/|SNRT |). The number of terminated users from service s is given by bcs /bcs . B. Admission Control for Handoff Requests Let αic and βic denote the parameters that define the threshold values after which connection requests from handoff users of each type will either be accepted or not in cell i ∈ Mc . Our proposed admission algorithm assigns the values of αic and βic based on the reserved BBUs and sets the priority for admission control among handoff requests according to the mobility scenario described in Section II. Thus, we have
cc s∈S j∈Aci hjis c c δic ∀ i ∈ Mc (15) αi = c s∈S φis − λis βic = δic − αic
∀ i ∈ Mc .
(16)
αic
The value of parameter is assigned based on the corresponding horizontal handoff rates. If the number of connection requests from horizontal handoff users increases, then more resources are allocated, and hence, higher priority is given to that type of handoff users, and vice versa. Both parameters αic and βic have integer values and 0 < αic ≤ δic . Note that the denominator in (15) considers all types of handoff requests. There are three different cases to consider in the proposed admission algorithm. In case 1 (αic > βic ), horizontal handoffs will have the highest priority for admission control, and they will always be accepted as long as there is capacity available in the cell. In case 2 (αic < βic ), vertical handoffs will have the highest priority for admission control. In case 3 (αic = βic ), both horizontal and vertical handoffs are equally important. In all three cases, the connection requests from the new users will have the lowest priority for admission control. These three cases and the corresponding handoff priorities for service s ∈ SRT in cell i ∈ Mc are shown in Fig. 3. Our proposed admissioncontrol algorithms using VP with preemption for horizontal and vertical handoff requests are shown in Algorithms 2 and 3, respectively. Algorithm 2—Admission control for horizontal handoff request with bandwidth requirement bcs in cell i ∈ Mc . 1: if αic ≥ βic , then 2: if s ∈SRT c c c 3: if s ∈SNRT mis bs > NNRTi c c c 4: if s ∈SRT mis bs + bs + ( s ∈SNRT mcis bcs − c c NNRTi ) ≤ NRT , i 5: then accept 6: else accept with preemption
c , 7: else if s ∈SRT mcis bcs + bcs + ≤ NRT i 8: then accept 9: else reject 10: if s ∈ SNRT , s ∈S mcis bcs + bcs ≤ Nic , 11: then accept 12: else reject 13: else if αic < βic , then 14: if s ∈SRT c c c 15: if s ∈SNRT mis bs > NNRTi c c c 16: if s ∈SRT mis bs + bs + ( s ∈SNRT mcis bcs − c c − βic , NNRTi ) ≤ NRT i 17: then accept 18: else if ( s ∈S mcis bcs ≥ Nic − c − βic ), βic , s ∈SRT mcis bcs + bcs ≤ NRT i 19: then accept with preemption. 20: else reject c − βic , 21: else if s ∈SRT mcis bcs + bcs ≤ NRT i 22: then accept 23: else reject 24: if s ∈ SNRT , s ∈S mcis bcs+bcs ≤ Nic−βic , then accept 25: else reject 26: end
Algorithm 3—Admission control for vertical handoff request with bandwidth requirement bcs in cell i ∈ Mc . 1: if αic > βic , then 2: if s ∈SRT c c c 3: if s ∈SNRT mis bs > NNRTi c c c 4: if s ∈SRT mis bs + bs + ( s ∈SNRT mcis bcs − c N − αic , NNRTi ) ≤ NRT i 5: then accept 6: else if ( s ∈S mcis bcs ≥ Nic − c αic , s ∈SRT mcis bcs +bcs ≤ NRT − αic ), i 7: then accept with preemption. 8: else reject c − αic , 9: else if s ∈SRT mcis bcs + bcs ≤ NRT i 10: then accept 11: else reject 12: if s ∈ SNRT , s ∈S mcis bcs + bcs ≤ Nic − αic , 13: then accept 14: else reject 15: else if αic ≤ βic , then 16: if s ∈SRT c c c 17: if s ∈SNRT mis bs > NNRTi c c c 18: if s ∈SRT mis bs + bs + ( s ∈SNRT mcis bcs − c c , NNRTi ) ≤ NRT i 19: then accept 20: else if s ∈S mcis bcs + bcs > Nic , then accept with preemption 21: else reject c , then accept 22: else if s ∈SRT mcis bcs + bcs ≤ NRT i 23: else reject 24: if s ∈ SNRT , s ∈S mcis bcs + bcs ≤ Nic , then accept 25: else reject 26: end
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STEVENS-NAVARRO et al.: HANDOFF MANAGEMENT AND ADMISSION CONTROL USING VP WITH PREEMPTION
Fig. 3.
437
Priorities of the different connection requests of service s ∈ SRT in cell i ∈ Mc . Case 1 (αci > βic ), case 2 (αci < βic ), and case 3 (αci = βic ).
For connection requests from service s ∈ SRT in cell i ∈ c BBUs in cell i ∈ Mc can be used as Mc , in case 1, NRT i c c follows: NRTi − δi BBUs can be used for connection requests from either new, horizontal, or vertical handoff users, βic BBUs can be used for connection requests from either horizontal or vertical handoff users, and αic BBUs can be used for requests from horizontal handoff users. When the NRT group is a horizontal handoff request is accepted if underloaded, c c c c 2, step 7), and a s ∈SRT mis bs + bs ≤ NRTi (see Algorithm vertical handoff request is accepted if s ∈SRT mcis bcs + bcs ≤ c − αic (see Algorithm 3, step 9). On the other hand, in NRT i case 2, αic BBUs can be used for connection requests from either horizontal or vertical handoff users, and βic BBUs can be used for requests from vertical handoff users. When the NRT group a horizontal handoff request is accepted is underloaded, c c c m b + bcs ≤ NRT − βic (see Algorithm 2, if is s s ∈SRT i step 21), and a vertical handoff request is accepted if c c c c m b + b ≤ N (see Algorithm 3, step 22). In s is s RTi s ∈SRT case 3, a horizontal or a vertical handoff request is accepted c (see Algorithm 2, step 7 and if s ∈SRT mcis bcs + bcs ≤ NRT i Algorithm 3, step 22). If the NRT group is overloaded, we need to consider the similar situations as described for the new requests. If the total amount of resources usedby the RT users, the overloaded part c ), and the of the NRT users (i.e., s ∈SNRT mcis bcs − NNRT i c − βic or handoff connection is less than or equal to NNRT i c c NNRTi − αi , then the connection is accepted (see Algorithm 2, step 16 or Algorithm 3, step 4, respectively). Otherwise, preemption is invoked. We define preemption rules for the handoff requests according to the assigned priorities (see Fig. 3), which are given by each case (e.g., αic > βic ). For the horizontal handoff requests, we have rules for αic ≥ βic (see Algorithm 2, step 6) and αic < βic (see Algorithm 2, step 18). For the vertical handoff requests, we have rules for αic > βic (see Algorithm 3, step 6) and αic ≤ βic (see Algorithm 3, step 20). For connection requests from service s ∈ SNRT in cell i ∈ c 1, a horizontal handoff request is accepted if M , in case c c c c m b is s + bs ≤ Ni (see Algorithm s ∈S 2, step 10), and a vertical handoff request is accepted if s ∈S mcis bcs + bcs ≤ Nic − αic (see Algorithm 3, step 12). On the other hand, in handoff request is accepted if case c2, ca horizontal c c m b + b ≤ N − βic (see Algorithm s is s i s ∈S 2, step 24), and a vertical handoff request is accepted if s ∈S mcis bcs + bcs ≤ Nic (see Algorithm 3, step 24). Finally, in case 3, a horizontal or a vertical handoff request is accepted if
mcis bcs + bcs ≤ Nic (see Algorithm 2, step 10 and Algorithm 3, step 24, respectively). The admission algorithms in cell k ∈ Me define similar parameters δke , αke , and βke for the connection requests from the new, horizontal, and vertical handoff users. s ∈S
C. Connection-Level Model We model the occupancy of cells i ∈ Mc and k ∈ Me as |S|-dimensional Markov chains. Let mci = (mci1 , mci2 , . . . , mci|S| ) and mek = (mek1 , mek2 , . . . , mek|S| ) denote the occupancy vectors in cells i ∈ Mc and k ∈ Me , respectively. They indicate the number of connections of each service. Thus, the statespace of each cell is restricted to c c c e e e c c s∈S mis bs ≤ Ni and s∈S mks bs ≤ Nk . Let φis (mi ) and e e φks (mk ) denote the total arrival rates of connection requests of service s ∈ SRT considering the admission algorithms to cells i ∈ Mc and k ∈ Me , respectively. We then have (17), shown at the bottom of the next page. Similar equations can be derived for φeks (mek ) [22]. For the total arrival rates of connection requests of service s ∈ c with Nic in SNRT to cell i ∈ Mc , we simply replace NRT i . The departure rates are defined as (17) and SRT with SNRT μcis (mci ) = mcis μcis for s∈S bcs mcis ≤ Nic . Let Pic (mci ) and Pke (mek ) denote the steady-state probabilities of being in states mci in cell i. We can state the global balance equations for the Markov process in cell i ∈ Mc as
φcis (mci ) + Φcis (mci ) + μcis (mci ) Pic (mci ) s∈S
=
Pic (mci − s ) φcis (mci − s )
s∈S
+
s∈S
+
Pic (mci + s ) μcis (mci + s )
s∈SNRT s ∈SRT
s ∈ 1,...,
b
Pic (mci + s s − s )
s bs
× Φcis (mci + s s − s ) where s is an |S|-dimensional vector of zeros but with 1 in the sth position. The term Φcis (mci ) is controlled by the VP preemption rules and is defined in (18), shown at the bottom of the next page.
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The terms Φcis (mci ) in the global balance equations incorporate the additional state transitions due to preemption of RT connections over NRT connections. Note that, in all cases in (18), the NRT group shall be overloaded. For notation convenience, we enumerate the services as S = {1, 2, . . . , p, p + 1, . . . , |S|}. The RT services correspond to service 1 to service p, and the NRT services correspond to service p + 1 to service |S|. Now, the probability of blocking connection requests from a new user of service s ∈ SRT in cell i ∈ Mc following VP with preemption is Nc
RTi bc 1
Bnc is =
Nc
−δ c i RTi bc 1
mci = 1
Nc− i
mc b c i s s
Nc
−δ c i RTi bc p
Nc− i
s =1 bc |S|
···
mci
|S|
Nc
−δ c i RTi bc 1
+
−1
mc b c i s s =1 s bc p
Bnc is =
mci =0 1
⎧ c λis , ⎪ ⎪ ⎪ ⎪ cc ⎪ ⎪ hjis , ⎪ ⎪ c ⎪ ⎪ ⎨ j∈A i cc hjis , Φcis (mci ) = j∈Aci ⎪ ⎪ ⎪ ⎪ Ψec ⎪ is , ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Ψec is ,
s ∈S
=0
(19)
mci =0 p
Nc− i
p
mc b c i s s =1 s bc p+1
×
Nc− i
···
=0
|S|−1 s =1 bc |S|
mc b c i s s
mci
|S|
=0
if
For service s ∈ SRT , all vectors mci need to occupancy c c c − δic . satisfy the condition that s ∈SRT mis bs + bcs > NRT i On the other hand, for service s ∈ SNRT , all occupancy vectors
c mcis bcs ≤ NRT − δic i
s ∈SRT αic > βic
c and NRT − δic < i
c if αic < βic and NRT − δic < i c if αic = βic and NRT − δic < i c if αic > βic and NRT − αic < i c if αic < βic and NRT − βic < i
s ∈SRT
s ∈SRT
s ∈SRT
s ∈SRT
s ∈SRT
c mcis bcs ≤ NRT − αic i c mcis bcs ≤ NRT − βic i c mcis bcs ≤ NRT i
(17)
c mcis bcs ≤ NRT i c mcis bcs ≤ NRT i
otherwise
mcis bcs ≥ Nic − δic and
s ∈SRT
c mcis bcs + bcs ≤ NRT − δic i
mcis bcs + bcs > Nic , αic ≥ βic c c c if mis bs ≥ Nic − βic and mcis bcs + bcs ≤ NRT − βic , αic < βic i s ∈S s ∈SRT c c if mis bs + bcs > Nic , αic ≤ βic ∈S s c if mcis bcs ≥ Nic − αic and mcis bcs + bcs ≤ NRT − αic , αic > βic i if
(20)
s ∈S
−1
if
P c (mc ) λc × i c i ics . φis (mi )
p
if
|S|
···
1
mci =0
cc ⎧ c λis + hjis + Ψec ⎪ is , ⎪ c ⎪ j∈A ⎪ i ⎪ ⎪ ec ⎪ hcc ⎪ jis + Ψis , ⎪ c ⎪ j∈Ai ⎪ ⎪ ⎪ hcc + Ψec , ⎪ ⎪ jis is ⎪ ⎨ j∈Aci cc c c φis (mi ) = hjis + Ψec is , ⎪ c ⎪ j∈A ⎪ i ⎪ ⎪ ⎪ hcc ⎪ jis , ⎪ c ⎪ j∈A ⎪ i ⎪ ⎪ ⎪ Ψec ⎪ is , ⎪ ⎪ ⎩ 0,
mci
=0
mci =0
···
bc p
=0
p−1
mc b c i s s
···
RTi bc 1
p+1
Nc −δ c − i RTi
s =1 bc |S|
where the term λcis / s ∈S φcis (mci ) is the probability that the arrival is a new connection request of service s. For service s ∈ SNRT , the probability of blocking connection requests from a new user in cell i is c p−1 c c m b N − Nc i s RTi s =1 s
mci
|S|−1
s ∈S
P c (mc ) λc × i c i ics φis (mi ) s ∈S
Nc− i
P c (mc ) λc × i c i ics φis (mi )
=0
p+1
mc b c i s s
mc b c i s s =1 s bc p+1
mci
|S|−1
p
×
p
p+1
s =1 bc p
mci =
mc b c i s s =1 s bc p+1
mci
p−1
···
p
×
Nc − RTi
Nc− i
s ∈S
s ∈S
s ∈SRT
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STEVENS-NAVARRO et al.: HANDOFF MANAGEMENT AND ADMISSION CONTROL USING VP WITH PREEMPTION
mci need to satisfy the condition that s ∈S mcis bcs + bcs > Nic − δic . For the probability of dropping connection requests from a handoff user of service s in cell i ∈ Mc , according to the admission algorithms, we need to consider three cases. In case 1 (αic > βic ), the probability of dropping connection requests from horizontal handoff users of service s is c p−1 c c m b N − Nc i s RTi s =1 s RTi bc 1
mci =0 p
1
Nc− i
p
mc b c i s s =1 s bc p+1
×
mci
(mci )
×
s ∈S
Nc− i
|S|−1 s =1 bc |S|
mc b c i s s
mci
|S|
(21)
p
1
Nc− i
p
mc b c i s s =1 s c b p+1
×
mci
p+1
Pic
×
s ∈S
Nc− i
|S|−1 s =1 bc |S|
mc b c i s s
mci
=0
|S|
=0
(mci ) Ψec is φcis (mci )
(22)
RTi bc 1
mci = 1
×
Nc− i
−αc i RTi bc 1
c Dvh = is
p
mc b c i s s =1 s bc p+1
mci
p+1
=0
p
···
−αc i RTi bc p
Nc− i
s =1 bc |S|
mc b c i s s
mci
|S|
=0
−1
p
Nc− i
|S|−1 s =1 bc |S|
mc b c i s s
mci
|S|
=0
(23)
bc p
···
1
Nc− i
mci =0 p
p s =1 bc p+1
mc b c i s s
Pic
×
Nc− i
|S|−1 s =1 bc |S|
mc b c i s s
···
mci
=0
|S|
=0
(mci ) Ψec is . φcis (mci )
(24)
For service s ∈ SRT , all vectors mci need to occupancy c c . On satisfy the condition that s ∈SRT mis bcs + bcs > NRT i , all occupancy vectors mci the other hand, for service s ∈ SNRT c c c c need to satisfy the condition that s ∈S mis bs + bs > Ni . The probability of dropping connection requests from horizontal handoff users of service s ∈ SNRT is c p−1 c c m b N − Nc i s RTi s =1 s RTi bc 1
bc p
c Dhh = is
···
mci =0
mci =0 p
1
Nc− i
p
mc b c i s s =1 s bc p+1
|S|−1
mc b c i s s
mci =0
=0
mci =0
Nc mci =
bc p
···
RTi bc
···
s =1
(mci ) Ψec is . φcis (mci )
1
bc p
Nc
p−1
For service s ∈ SRT , all occupancy vectors mci need to satc − αic . On isfy the condition that s ∈SRT mcis bcs + bcs > NRT i all occupancy vectors the other hand, for service s ∈ SNRT , mci need to satisfy the condition that s ∈S mcis bcs + bcs > Nic − αic . In case 2 (αic < βic ), the probability of dropping connection requests from vertical handoff users of service s is c p−1 c c m b N − Nc i s RTi s =1 s
s ∈S
p+1
c c where the term Ψec is / s ∈S φis (mi ) is the probability that the arrival is a vertical handoff request of service s. For service s ∈ SRT , the probability of dropping connection requests from vertical handoff users is c p−1 c c m b N − Nc i s RTi s =1 s c Dvh = is
mc b c i s s =1 s bc p+1
p+1
···
···
mci
Nc −αc − i RTi
p
×
mci =0
−1
mci
bc p
···
Nc− i
×
mci =0
s ∈S
(mci )
1
×
=0
mci =0
Pic
hcc jis
RTi bc 1
+
c c where the term j∈Ac hcc jis / s ∈S φis (mi ) is the probability i that the arrival is a horizontal handoff request of service s. For service s ∈ SRT , all vectors mci need to occupancy c c . On satisfy the condition that s ∈SRT mis bcs + bcs > NRT i the other hand, for service s ∈ SNRT , all occupancy vectors mci c c c c need to satisfy the condition that s ∈S mis bs + bs > Ni . The probability of dropping connection requests from vertical handoff users of service s ∈ SNRT is c p−1 c c m b N − Nc i s RTi s =1 s c Dvh = is
−αc i RTi bc 1
···
j∈Aci
φcis
=0
p+1
Pic
Nc
···
mci =0
s ∈S
bc p
c = Dhh is
P c (mc ) Ψec × i c i ics φis (mi )
439
×
mci
p+1
Pic (mci ) ×
s ∈S
···
j∈Aci
Nc− i
|S|−1 s =1 bc |S|
mc b c i s s
mci
=0
|S|
=0
hcc jis
φcis (mci )
.
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 1, JANUARY 2010
For service s ∈ SRT , the probability of dropping connection requests from horizontal handoff users is Nc
RTi bc 1
c Dhh = is
Nc
−β c i RTi bc 1
mci = 1
Nc− i
−β c i RTi bc 1
−1
1
Nc− i
p
mc b c i s s =1 s bc p+1
Nc− i
mci =0 p+1 cc (mci ) hjis j∈Aci
s ∈S
φcis (mci )
|S|−1 s =1 bc |S|
mci
|S|
Nc −β c − i RTi
mc b c i s s
p−1 s =1 bc p
=0
mc b c i s s
−1
×
···
mci =0
Pic
···
φcis (mci )
Nc +
−β c i RTi bc p
p
mci =0 p+1 cc (mci ) hjis j∈Aci
s ∈S
mc b c i s s
Nc mci =
mc b c i s s =1 s bc p+1
×
s =1 bc p
Pic
p−1
···
p
×
×
Nc − RTi
···
mci =0 Nc− i
p |S|−1 s =1 bc |S|
mci
|S|
.
mc b c i s s
=0
(26)
For service s ∈ SRT , all occupancy vectors mci need to c − βic . satisfy the condition that s ∈SRT mcis bcs + bcs > NRT i all occupancy vectors On the other hand, for service s ∈ SNRT , mci need to satisfy the condition that s ∈S mcis bcs + bcs > Nic − βic . In case 3 (αic = βic ), the probability of dropping connection requests from horizontal handoff users of service s can be calculated as in (22). The probability of dropping connection requests from vertical handoff users of service s can be calculated c as in (23). For service s ∈ S RT , all occupancy vectors mi need c c c c to satisfy the condition that s ∈SRT mis bs + bs > NRTi . On vectors mci the other hand, for service s ∈ SNRT , all occupancy c c need to satisfy the condition that s ∈S mis bs + bcs > Nic . Similar admission policy and preemption rules are applied in the IEEE 802.16e network. Thus, for cell k ∈ M e in the global balance equations, the probabilities for blocking new users and dropping horizontal and vertical handoff users can similarly be derived with the corresponding IEEE 802.16 parameters [22]. cc , Given the network parameters λcis , λeks , ηic , ηke , μcis , μeks , qij s ce ee ec c e c qils , qkls , qkjs , υs , bs , and bs for {i, j} ∈ M , {k, l} ∈ Me , and s ∈ S, we can solve equations in the model at the connection level and obtain the blocking and dropping probabilities c c e e , Dvh , Bne ks , Dhh , and Dvh for i ∈ Mc , Bnc is , Dhh is is ks ks e k ∈ M , and s ∈ S. Note that to compute the arrival rates, we need to solve the set of fixed-point equations given by the handoff rate equations. We can use the iterative fixed-point algorithm of repeated substitutions [27].
D. Packet-Level Model At the packet level, for i ∈ Mc and k ∈ Me , the performance metric of interest is the probability of packet loss. We consider that packet loss can occur when the total number of required BBUs from the active connections exceeds the capacity of the cell. Thus, let Lcis and Leks denote the packetloss probabilities experienced by connections of service s due to statistical multiplexing in cells i and k, respectively. To calculate Lcis and Leks , we assume that once a connection is accepted, it behaves as an exponentially distributed ON–OFF traffic source. The ON–OFF traffic model can be used to model voice, bursty data, and video sources [28], [29]. A source from service s requires three parameters to represent it: the transmission rate bcs , the average time that the source is in the ON state (i.e., the burst length) tONs , and the fraction of time that the source is in the ON state or the activity factor ρs . To model traffic sources as ON–OFF sources, we follow the methodology described in [29]. Further details are given in Section IV. This model is general enough to capture the behavior where the performance is mainly determined by the burst level of the sources. In this case, we are interested in the situation when the aggregated traffic from the active connections (i.e., in the ON state) exceeds the capacity. Thus, when a connection of service s in cell i ∈ Mc (k ∈ Me ) is in the ON state, it generates packets at a rate that requires bcs BBUs (bes BBUs) to transmit the packets. In any network, the fraction of time that a connection spends in the ON state is given by ρs = tONs /(tONs + tOFFs ), where tOFFs is the time that the connection is in the OFF state. ¯ eks denote the numbers of connections in the Let m ¯ cis and m ON state in cells i ∈ Mc and k ∈ Me , respectively. Then, the ¯ eks connections of service probabilities that there are m ¯ cis and m s in the ON state, given that there are mcis and meks connections in each cell, are given by c c c mis j c P m ¯ is = j | mis = ρs (1−ρs )mis −j , 0 ≤ j ≤ mcis j (27) e e e m ks P m ¯ ks = j | meks = ρjs (1−ρs )mks −j , 0 ≤ j ≤ meks . j (28) Packet loss can occur in a cell when the total number of BBUs required from the connections in the ON state exceeds ¯ cis bcs > Cic ). Recall that the capacity of the cell (i.e., s∈S m parameters Nic and Nkw must not be less than the capacities of the cells. Considering that the RT connections have priority over the NRT connections, the packet-loss probability due to statistical multiplexing for service s connections in cell i ∈ Mc is ⎥ ⎢ ⎢ N c −|S|−1 mc bc ⎥ ⎥ ⎢ i i s s =1 s ⎦ ⎣ c bc N i bc
1
Lcis =
mci =0 1 mci
|S|
···
mci =0 |S|
mc
Pic (mci )
i1
···
m ¯ ci =0 1
Θ (m c c is ¯ i ) ¯ ci|S| mci|S| P m ¯ i1 mci1 · · · P m c P S li =0
|S|
m ¯ ci
|S|
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STEVENS-NAVARRO et al.: HANDOFF MANAGEMENT AND ADMISSION CONTROL USING VP WITH PREEMPTION
¯ ci ) is defined in (30), shown at the bottom of the where Θcis (m + page, [a] = max[a, 0], and ⎥ ⎢ ⎢ N c −|S|−1 mc bc ⎥ ⎥ ⎢ i i s =1 s s ⎦ ⎣ c bc N i bc 1
|S|
P Slci =
···
mci =0 1 mci |S| m ¯ ci
|S|
Pic (mci )
mci =0 |S|
···
m ¯ ci =0 1
(31)
s ∈S
=0
In (30), if the nominal allocation for the RT group is less c ≤ Cic ), then than or equal to the capacity of the cell (i.e., NRT i the connections from the RT group will not experience packet loss due to statistical multiplexing. Finally, the same packetloss model considering statistical multiplexing is used for cell k ∈ Me . E. Joint Connection- and Packet-Level QoS Optimization To select the design parameters Nic in cell i ∈ Mc and Nke in cell k ∈ Me , a joint connection- and packet-level QoS optimization approach is used. We propose the following blocking/ dropping cost minimization problem with constraints at the connection level in terms of blocking and dropping probabilities and at the packet level in terms of packet-loss probability. The objective is to minimize all penalty costs involved in the blocking and dropping of connections. Note that cost minimization is equivalent to revenue maximization. We define the objective function, which is a linear combination of the blocking and dropping probabilities, i.e., ! c c c c c c ω B +ω D +ω D minimize nis nis hhis hhis vhis vhis c e Ni , Nk
s∈S i∈Mc
" e e e e + ωne ksBne ks +ωhh Dhh +ωvh Dvh ks ks ks ks k∈Me
subject to
Bnc is
≤ Γcnis
Bne ks ≤ Γenks
∀ i ∈ Mc , s ∈ S
e Dvh ≤ Γevhks ks
∀ k ∈ Me , s ∈ S
1
c ¯ ci|S| |mci|S| P m ¯ i1 |mci1 · · · P m m ¯ cis bcs .
c ≤ Γcvhis Dvh is
mci
∀ i ∈ Mc , s ∈ S ∀ k ∈ Me , s ∈ S
c Dhh ≤ Γchhis is
∀ i ∈ Mc , s ∈ S
e Dhh ≤ Γehhks ks
∀ k ∈ Me , s ∈ S
441
Lcis ≤ Γcpis
∀ i ∈ Mc , s ∈ S
Leks ≤ Γepks
∀ k ∈ Me , s ∈ S
(32)
where ωnc is and ωne ks denote the cost of blocking a connection request for service s from a new user in cells i and k, c e c e , ωhh , ωvh , and ωvh denote respectively. Similarly, ωhh is is ks ks the costs of dropping a connection request for service s from a horizontal and a vertical handoff user in cells i and k, respectively. To ensure that higher priority is considered for accepting connection requests from handoff users rather than c and ωnc is < new users, it is reasonable to set ωnc is < ωhh i c c e e s ωvhis for all i ∈ M and s ∈ S, and ωnks < ωhhks and ωne ks < e for all k ∈ Me and s ∈ S. At the connection level, Γcnis ωvh ks e and Γnks are the maximum blocking probabilities allowed for new connection requests from service s, Γchhis and Γehhks are the maximum dropping probabilities allowed for horizontal handoff requests from service s, and Γcvhis and Γevhks are the maximum dropping probabilities allowed for vertical handoff requests from service s in cells i and k, respectively. Finally, at the packet level, Γcpis and Γepks are the maximum packet-loss probabilities allowed for connections from service s in cells i and k, respectively. IV. P ERFORMANCE E VALUATION We evaluate the performance of an integrated cellular/ 802.16e system consisting of a 3G RAN with |Mc | = 12 cells and an 802.16e ASN with |Me | = 3 cells. As shown in Fig. 2, the cells are labeled as follows: Mc = {C1, C2, C3, . . . , C12}, and Me = {E1, E2, E3}. At the connection level, we consider different traffic patterns by assigning different values to parameters λcis and λeks . Three different services are considered: two RT multimedia services (i.e., SRT = {1, 2}) and one NRT data service (i.e., SNRT = {3}). The connection durations have means 1/υ1 = 1/υ2 = 6 min, and 1/υ3 = 4 min. In the integrated system, cells are of the same size [3]. The interboundary times in cells i and k have means 1/ηic = 1/ηke = 4 min. Different levels of mobility of users are also investigated. In each cell i ∈ Mc , the network capacity is 2 Mb/s, and the BBU is set to 32 kb/s based on the 3GPP-supported multimedia bearer services [30]. This implies that the capacity of each cell is Cic = 62 BBUs. The first service, i.e., s = 1, is voice
⎧ m ¯ cis bcs , ⎪ ⎪ ∈S ⎪ s ⎪ ! NRT " ⎪ ⎪ + ⎪ ⎪ ⎪ c c c c c ⎪ m ¯ is bs − Ci − s ∈SRT m ¯ is bs , ⎪ ⎨ s ∈S NRT c c ¯ i) = ! Θis (m "+ ⎪ ⎪ ⎪ c c c ⎪ m ¯ is bs − Ci , ⎪ ⎪ ⎪ s ∈SRT ⎪ ⎪ ⎪ ⎪ ⎩ 0,
if
s ∈SRT
if
s ∈SRT
if
s ∈SRT
if
s ∈SRT
m ¯ cis bcs > Cic and s ∈ SNRT m ¯ cis bcs ≤ Cic and s ∈ SNRT (30) m ¯ cis bcs
>
Cic
and s ∈ SRT
m ¯ cis bcs ≤ Cic and s ∈ SRT
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connections requiring 32 kb/s. The second service, i.e., s = 2, is video connections requiring 64 kb/s. These values are set according to the multimedia codecs for 3GPP [31]. The third service, i.e., s = 3, is data connections with Hypertext Transfer Protocol traffic (i.e., web browsing) at 32 kb/s. Thus, QoS provisioning in cell i stipulates that bc1 = 1 BBU, bc2 = 2 BBUs, and bc3 = 1 BBU. In each cell k ∈ Me , according to [23], the network capacity is 6 Mb/s. To benefit from the additional capacity, the required data rates of the services are reasonably assumed to be larger in the 802.16e ASN than the rates in the 3G RAN. We set the BBU to 64 kb/s, the voice connections to 64 kb/s, video connections to 128 kb/s, and data connections to 64 kb/s. This implies that the capacity of each cell k is Cke = 92 BBUs and that QoS provisioning is be1 = 1 BBU, be2 = 2 BBUs, and be3 = 1 BBU. Based on the defined QoS provisioning (i.e., bc1 = 1, bc2 = 2, and bc3 = 1) and according to [15], we set the nominal alloc c , NNRT ) = (3, 1)Nic /4 and δic = 4. cations in cell i as (NRT i i The same nominal allocations apply to cell k and δke = 6. To set the integer values of Nic and Nke , we solve the cost minimization problem in (32) by using an exhaustive search algorithm. Note that, to have a statistical multiplexing gain, the search is restricted to Nic > Cic and Nke > Cke . As in [20], we set for all cell i ∈ Mc , cell k ∈ Me , and s ∈ S, ωnc is = c e c e = ωhh = 10, and ωvh = ωvh = 10. The ωne ks = 1, ωhh is is ks ks QoS constraints are as follows: Γcni = 0.05, Γchhi = Γcvhi = 1 1 1 0.05, Γcni = 0.20, and Γchhi = Γcvhi = 0.1 for all cell 2/3
2/3
Fig. 4. Comparison between analytical and simulation results for the new connection blocking probability in cells C1 and E1 versus the arrival rate of connection requests from service 2.
2/3
i ∈ Mc . The same values are set in cell k ∈ Me . Finally, at the packet level, for service s = 1, the average TON1 = 7.24 s and TOFF2 = 5.69 s. Thus, ρ1 = 0.54 [32]. For service s = 2, we assume video frames with an average size Favg = 300 bytes, which arrive at periodic time intervals every 1/24 s. Thus, ρ2 = (Favg /bc2 )/(1/24) = 0.90 [29]. For service s = 3, we assume Web pages with an average size of 100 kB and an average TOFF3 (i.e., reading time) of 30 s. Thus, ρ3 = 0.45 [33]. The QoS constraints are Γcpis = Γepks = 5 × 10−5 for all cell i ∈ Mc , cell k ∈ Me , and s ∈ S. Fig. 5. New connection blocking probability in cells C1 and E1 versus arrival rate of connection requests from service 2.
A. Effect of Increasing the Arrival Rate For analytical model validation, a discrete event-driven network simulator is created using MATLAB. Simulations results are then compared with the results obtained from the analytical model. The simulation results are averaged over 500 simulation runs. The simulation time for each run is 106 min. Thus, if the arrival rate is 1.5 requests/min, then there are 1.5 × 106 service requests generated in the system for each cell. The blocking probabilities in each simulation run are calculated based on the ratio of the total number of rejected connection requests and the total number of requests. Fig. 4 shows the new connection blocking probability of service 2 for cells C1 and E1 versus the arrival rate of service 2. Fig. 4 shows that the analytical results closely matched the simulation results. Next, we present the results obtained from the analytical models. Fig. 5 shows the probability of blocking connection requests from the new users of the three services in cells C1 and E1. The arrival rate of connection requests from service 2
is increased from 0.2 to 2 connection requests per minute, whereas the arrival rates of services 1 and 3 remain constant at 1 connection request per minute. For the following results, we set λs = λcsi = λesk (i.e., the same increase of connection requests occurs in the 3G RAN and the 802.16e ASN). In both networks, the blocking probabilities for new connection requests of service 2 are the highest, since such connections require twice as many BBUs than services 1 and 3. On the other hand, note that the blocking probabilities for new connection requests of service 1 are lower than those for service 3. The reason is that the connections from service 1 belong to the RT group (i.e., SNRT = {1, 2}), which can preempt the connections from the NRT group (i.e., SNRT = {3}). Thus, due to preemption, the new requests from service 1 are able to obtain access to the integrated cellular/802.16e system more often than those from service 3. Fig. 5 also shows that the blocking probabilities in cell E1 of the 802.16e ASN are lower than those in cell C1
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Fig. 6. Horizontal handoff-dropping probability in cells C1 and E1 versus arrival rate of connection requests from service 2.
Fig. 7. Vertical handoff-dropping probability in cells C1 and E1 versus arrival rate of connection requests from service 2.
due to the higher capacity in the 802.16e ASN compared with the 3G RAN. Figs. 6 and 7 show the probabilities of dropping connection requests of the three services in cells C1 and E1 from horizontal and vertical handoff users, respectively. In both networks, the highest probabilities correspond to the connection requests from service 2, followed by those of services 3 and 1 in decreasing order. Note also that the dropping probabilities in cell C1 for horizontal handoffs are lower than those for vertical handoffs. On the other hand, the dropping probabilities in cell E1 for horizontal handoffs are higher than those for vertical handoffs. c c > βC1 ) The reason is that, in cell C1, we have case 1 (αC1 e e from Fig. 3, whereas in cell E1, we have case 2 (αE1 < βE1 ). This is expected since, as described in Section III, each case depends on the handoff rates from the mobility scenario. This can also be seen from Fig. 2. Cell C1 of the 3G RAN with c = {E1} receives horizontal handoff requests from six WC1 adjacent cells AcC1 = {C2, C3, C7, . . . , C10}, but it only re-
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Fig. 8. Packet-loss probability in cells C1 and E1 versus arrival rate of connection requests from service 2.
ceives optional and transferred vertical handoffs requests from two cells AeE1 = {E2, E3}. Cell E1 of the 802.16e ASN with e = {C1} receives horizontal handoff requests from only WE1 two adjacent cells and also receives optional and transferred vertical handoffs requests from six cells. Fig. 8 shows the probability of packet loss for connections of service 3 in cells C1 and E1. In both networks, the nominal allocations for the connections from the RT group, c e = 58 and NRT = 87, respectively, are less than i.e., NRT C1 E1 c = 62 and the corresponding capacities of their cells, i.e., CC1 e CE1 = 92, respectively. Such connections do not experience packet loss due to statistical multiplexing. On the other hand, we can see that as the arrival rate of connection requests from service 2 increases, service 3 starts to experience a considerable increase on the packet-loss probability in both networks. Recall that theconnections from the NRT group can only ¯ cis bcs ≤ Cic in (30). Fig. 8 also shows transmit when s∈SRT m the performance of the algorithm when the packet-interarrival time follows a Pareto distribution instead of an exponential distribution. The Pareto distribution has two parameters. We set the shape parameter to be equal to 3 and vary the scaling parameter such that the average packet-interarrival time for both Pareto and exponential distributions is equal. Results show that the packet-loss probability is slightly reduced when the packetinterarrival time follows a Pareto distribution. B. Performance Comparison With a Fixed Policy Fig. 9 shows the probability of dropping connection requests from horizontal and vertical handoff users of service 1 in cell C1 of the 3G RAN. We compare the performance of the integrated cellular/802.16e system operating as described in Section III versus the system operating with a fixed policy. When the fixed policy is used, the system is operating as c c = βC1 ) at all times and independent from in case 3 (αC1 the handoff rates of the mobility scenario. The rest of the parameters are set the same as before. In Fig. 9, we can see that the horizontal handoff-dropping probabilities are 170%
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Fig. 9. Horizontal and vertical dropping probabilities in cell C1 versus arrival rate of connection requests from service 2. Performance comparison with a fixed policy.
Fig. 10. New connection blocking probability in cell E1 versus arrival rate of connection requests from service 2. Comparison between with and without using joint connection- and packet-level QoS optimization.
higher when the fixed policy is used. On the other hand, the vertical handoff dropping probabilities are 55% lower when such fixed policy is used. As explained before, since the system c e > βC1 ) (i.e., cell C1 receives is operating in case 2 (αC1 more requests from horizontal handoff users than from vertical handoff users), higher priority is given to connection requests from horizontal handoff users and less priority to the requests from vertical handoff users. This translates into lowering the horizontal handoff dropping probabilities at the expense of slightly increasing the vertical handoff-dropping probabilities. This expense is compensated by the fact that fewer vertical handoff requests will arrive at cell C1. Nevertheless, we can see that the horizontal handoff-dropping probabilities are reduced by 63% when the system operates in case 2, as compared with the case when the system operates with the fixed policy.
e CE1 . However, the packet-loss probabilities can be bounded into a suitable value due to the packet-level constraints in the joint QoS optimization problem in (32).
C. Joint QoS Optimization Fig. 10 shows the probability of blocking connection requests from the new users of services 1 and 2 in cell E1. We compare the performance of the integrated cellular/802.16e system without using the joint connection- and packet-level optimization. The parameters Nic and Nke are set as the capacities Cic and Cke , respectively. In Fig. 10, we can see that the blocking probabilities increase faster for service 2. The reason is that we are increasing the arrival rate of service 2, whereas the arrival rates of services 1 and 3 remain constant. Moreover, connection requests from service 2 require more BBUs. The blocking probabilities of connections from services 1 and 2 are 66% and 70% lower, respectively, when the parameters Nke are set from the joint QoS optimization approach. It is worth mentioning that this decrease in the blocking probabilities at the connection level should be traded off against tolerating an increase on the packet-loss probabilities. However, for the case Nke = Cke , there is no packet loss due to statistical multiplexing at the packet level for neither of the groups (i.e., RT and NRT) because we always have the condition that s∈S meE1s bes ≤
V. C ONCLUSION In this paper, we have first described the mobility scenario for 3G cellular/802.16e interworking. The scenario specified the horizontal and vertical handoffs that can occur in such integrated system. We have extended the VP with preemption technique to be used for admission control in cellular/802.16e interworking. To this end, we have proposed admission-control algorithms for connection requests that consider the class of service (i.e., RT or NRT) and the type of user (i.e., new or handoff). Both horizontal and vertical handoffs have been considered, and suitable preemption rules have been defined for the RT and NRT connections. We have formulated a blocking/dropping cost-minimization problem following a joint connection- and packet-level QoS optimization approach. The analytical results have been validated via simulations. Results show the performance of the integrated system in terms of the probability of blocking new connection requests, the probability of dropping horizontal and vertical handoff connection requests, and the probability of packet loss. Performance improvement is shown at the connection level when the proposed admission algorithms are used compared with a fixed policy since they properly assign the priorities for admission control to each type of handoff user based on the described mobility scenario. Improvement is also shown when preemption of RT connections over NRT connections and the joint QoS optimization are used. R EFERENCES [1] D. Niyato and E. Hossain, “Call admission control for QoS provisioning in 4G wireless networks: Issues and approaches,” IEEE Netw., vol. 19, no. 5, pp. 5–11, Sep./Oct. 2005. [2] Amendment. Part 16: Air Interface for Fixed Broadband Wireless Access Systems—Physical and Medium Access Control Layers for Combined
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[29] Y. Xu and R. Guerin, “Individual QoS versus aggregate QoS: A loss performance study,” IEEE/ACM Trans. Netw., vol. 13, no. 2, pp. 370–383, Apr. 2005. [30] 3GPP, Circuit Bearer Services Supported by a Public Land Mobile Network, Jun. 2007, TS 22.002 (ver. 7.0.0). [31] 3GPP, Codecs for Circuit Switched Multimedia Telephony Service, Jun. 2007, TS 26.110 (ver. 7.0.0). [32] S. Deng, “Traffic characteristics of packet voice,” in Proc. IEEE ICC, Seattle, WA, Jun. 1995, pp. 1369–1374. [33] S. Deng, “Empirical model of WWW document arrivals at access link,” in Proc. IEEE ICC, Dallas, TX, Jun. 1996, pp. 1797–1802.
Enrique Stevens-Navarro (S’99–M’09) received the B.Sc. degree in electrical engineering from the Universidad Autonoma de San Luis Potosi (UASLP), San Luis Potosi, Mexico, in 2000, the M.Sc. degree in electrical engineering from the Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Mexico, in 2002, and the Ph.D. degree in electrical engineering from The University of British Columbia, Vancouver, BC, Canada, in 2008. From 2002 to 2003, he was a Project Manager with Q-Voz IVR Outsourcing, Monterrey. He is currently an Assistant Professor with the Faculty of Science, UASLP. His research interests are in mobility and resource management for heterogeneous wireless networks. Dr. Stevens-Navarro is a member of the Mexican National Research System.
Vahid Shah-Mansouri (S’02) received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2003 and the M.Sc. degree in electrical engineering from Sharif University of Technology, Tehran, in 2005. He is currently working toward the Ph.D. degree with the Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC, Canada. From 2005 to 2006, he was with Farineh-Fanavar Co., Tehran. His current research interests are in mathematical modeling and protocol design for radio-frequency identification systems and wireless sensor networks.
Vincent W. S. Wong (SM’07) received the B.Sc. degree from the University of Manitoba, Winnipeg, MB, Canada, in 1994, the M.A.Sc. degree from the University of Waterloo, Waterloo, ON, Canada, in 1996, and the Ph.D. degree from The University of British Columbia (UBC), Vancouver, BC, Canada, in 2000. From 2000 to 2001, he was a Systems Engineer with PMC-Sierra Inc. In 2002, he joined the Department of Electrical and Computer Engineering, UBC, where he is currently an Associate Professor. His research areas include protocol design, optimization, and resource management of communication networks, with applications to the Internet, wireless networks, radio-frequecy identification systems, and intelligent transportation systems. Dr. Wong is a member of the Association for Computing Machinery. He currently serves as an Associate Editor of the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY and an Editor of KICS/IEEE Journal of Communications and Networks. He serves as a Technical Program Committee Member for various conferences, including the IEEE Conference on Computer Communications (Infocom), the IEEE International Conference on Communications (ICC), and the IEEE Global Telecommunications Conference (Globecom).
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