2010 5th International Symposium on Wireless Pervasive Computing (ISWPC)
Joint BS Assignment and End-to-End Scheduling for Wireless Cellular Networks with Heterogeneous Services Walid Saad1 , Sanaa Sharafeddine2 , and Zaher Dawy1 1
American University of Beirut, Department of Electrical and Computer Engineering Beirut, Lebanon, Email: {wes02, zaher.dawy}@aub.edu.lb 2 Lebanese American University, Department of Computer Science and Mathematics Beirut, Lebanon, Email:
[email protected]
Abstract— In our previous work, we proposed and evaluated an end-to-end scheduling approach for allocating resources to mobile users with end-to-end delay requirements. The novelty of the proposed approach is that it ensures an end-to-end utility in terms of delay and frame success rate by simultaneously considering both the time varying channel conditions in the uplink and the downlink directions. In this work, we extend the end-to-end scheduling approach by designing and evaluating a joint scheduling and BS assignment algorithm in order to further improve the system performance. Moreover, we extend the system model to include heterogeneous services with varying quality parameters. Results show that the performance gains, in terms of higher average number of active connections and lower packet drop ratio, increase notably with joint BS assignment depending on the level of distribution of users in the network.
I. I NTRODUCTION Mobile services such as video conferencing and network gaming impose stringent quality requirements on wireless cellular networks. An appealing approach to meet these requirements is to jointly perform scheduling with base station (BS) assignment [1]. However, the mainstream literature on joint scheduling and BS assignment algorithms considers only single-link scenarios for either the uplink direction or the downlink direction. For instance, in [2] and [3], an SNRbased joint scheduling and BS assignment algorithm is derived for maximizing individual mobile station (MS) utilities in terms of uplink throughput. A priority based scheduler for optimizing uplink frame success rate (FSR) is given in [4]. A joint downlink scheduling and BS assignment algorithm is presented in [5] for a non-uniform CDMA network with two service classes, where non cooperative game theory is used in order to maximize the total utility per individual BS. For the downlink, another game theory based scheduling and BS assignment algorithm is presented in [6] where a utility function is defined per packet in terms of FSR. Finally, in [7] a centralized scheduler for selecting active users and BSs in the downlink is proposed. The previously mentioned algorithms focus on either uplink only or downlink only scenarios. Nevertheless, many personto-person mobile services such as video telephony, mobile network gaming, or file sharing require end-to-end delay and FSR guarantees between two communicating users: an uplink MS which is sending packets to a downlink MS inside the network. In [8] and [9], we have shown that in such scenarios single-link schedulers can be inefficient, and the performance can be significantly improved by using an end-to-end scheduling algorithm which schedules MSs in communicating pairs
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while jointly accounting for both the uplink and downlink channels. In [8], we proposed a micro-economics based endto-end scheduler for guaranteeing an end-to-end utility value for a CDMA network with single service class. In [9], we proposed a generic end-to-end scheduling algorithm for a single service CDMA cellular network which maximizes an end-to-end utility function that depends on end-to-end delay and FSR. In the previous work, we focused on a system model with a single service class and the BS assignment for the different MSs was distance-based. In this paper, we extend [9] by incorporating a joint BS assignment algorithm that accounts for the end-to-end communication link between the uplink and downlink MSs as well as for the load of each BS, prior to assigning MSs to their serving BSs. We show that by incorporating a joint BS assignment scheme, the performance of end-to-end scheduling can be significantly improved. Furthermore, we show that the proposed joint endto-end scheduling and BS assignment algorithm efficiently copes with the presence of heterogeneous services by allowing each service class to meet its specific quality requirements. The paper is organized as follows. Section II describes the system model while Section III presents the proposed joint end-to-end scheduling and BS assignment algorithm. Simulation results are presented and analyzed in Section IV. Finally, conclusions are drawn in Section V. II. S YSTEM M ODEL A. Network Model and Channel Quality We consider a time-slotted multi-cell CDMA cellular system having C BSs with 2K mobiles. The set of all BSs in the network is denoted by C = {1, 2, ...C}. The MSs are considered in communicating pairs referred to as “connections”. Each connection denotes two MSs involved in an end-to-end session whereby an uplink MS is sending packets to another MS receiving this packet in the downlink (the two MSs can be in the same or different cells). Each connection belongs to a particular service class s that determines its end-to-end delay and FSR requirements. Within a time slot of duration θ, we assume that an uplink MS transmits only one packet of length Ls to its corresponding downlink MS. The considered path loss model accounts for both distance based path loss and correlated shadowing (at BS and MS) with gi,ci as path loss attenuation between a MS i and its serving BS ci ∈ C. For channel quality, we use the FSR as the main metric. For a connection between an uplink MS i and downlink MS j, the SIR of MS i received by its BS ci ∈ C is given by
Γi,ci = Si,s Kc
gi,ci Pi,ci
(1) 2 g P + αP + σ k,c k,c R i i k=1,k=i where Si,s = W/Ri,s represents the uplink spreading factor (SF) determined by the connection’s service class s, W is the chip rate, Ri,s is the data rate of MS i belonging to service class s, Pi,ci is the transmit power of MS i, Kc PR = k=1i gk,ci Pk,ci is the total received power at BS ci , Kci is the number of active users served by BS ci , α is the intercell to intracell interference factor, and σ 2 is the variance of the additive Gaussian noise. Furthermore, the SIR of downlink MS j as received from its serving BS cj ∈ C is given by gj,cj Pj,cj γj,cj = Sj,s (2) λgj,cj (Pcj − Pj,cj ) + αj gj,cj Pcj + σ 2 where Sj,s = W/Rj,s represents the downlink SF determined by the connection’s service class s, W is the chip rate, Rj,s is the data rate of MS j belonging to service class s, Pj,cj is the transmit power allocated to MS j by BS cj for the transmission of the intended packet, Pcj is the total transmit power of BS cj , λ is the orthogonality factor, and αj is the intercell to intracell interference factor of MS j. B. End-to-End Delay The end-to-end delay model used is similar to [9] where queueing delay at the uplink MS is the main delay component for each connection. The connection’s service class s imposes a maximum tolerable end-to-end delay τs for every packet. After τs has elapsed the packet is dropped and the user receives a new packet from upper layers. Moreover, we define d as the remaining tolerable delay in a time slot for a particular transmission direction (uplink or downlink): (3) d = τs − qθ
˜l ul ≥ u
(5)
i
where θ is the duration of a time slot and q is the number of time slots elapsed since the packet was generated. C. Utility and Debt A utility function per direction (uplink or downlink) is defined as an increasing function of the FSR reflecting channel quality and a decreasing function of the remaining tolerable delay d (i.e. waiting time) reflecting the end-to-end delay. The FSR for a packet of length Ls is given by f = (1 − Pe )Ls where Pe is the bit error rate (BER). In consequence, the total “profit” experienced by the network for granting an end-to-end packet transmission opportunity for a connection l between MS i and MS j is captured by an end-to-end utility defined as (4) ul = vi + wj where vi and wj are the utilities of the uplink and downlink transmissions, respectively. For ensuring end-to-end QoS, the scheduler guarantees an end-to-end target utility value u˜l for every connection in the network. This target utility value is implied by the target FSR and target end-to-end delay required by the different network services. For the sake of guaranteeing both delay and channel quality, the scheduler will permit a trade-off of channel quality for the sake of transmitting in time while maintaining the target end-to-end utility value. For a connection l, this end-to-end utility guarantee maps into
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Equations (4) and (5) yield the following: for the uplink vi ≥ v˜i (6) ˜j for the downlink wj ≥ w ˜j are the target utilities for the uplink and where v˜i and w downlink, respectively. A minimum allowable FSR f˘s is defined as follows for every transmission direction: (7) f˘s = f˜s − εs where f˜s is the target FSR imposed by service class s, and εs is a margin FSR value which is set depending on the required minimum FSR of service class s. This minimum FSR enables the scheduler to provide a minimum FSR limit for the FSRdelay trade-off. Hence, the maximum FSR margin that the scheduler is allowed to trade off for the purpose of allowing a transmission in time is εs . Consequently, the minimum allowable FSR provides a minimum channel quality bound to be respected by the scheduling algorithm. The minimum FSR constraint for each connection leads to a minimum end-to-end utility value u ˘ per time slot. Finally, the debt δl of a connection l ia defined as the amount of end-to-end utility required by this connection in order to achieve its target utility value; consequently guaranteeing the required end-to-end QoS in terms of delay and FSR. Hence, the debt is given by ˜l − u ˘l (8) δl = u The value of δl allows the scheduler to assess the required resources that should be allocated in the uplink and the downlink for connection l in order to ensure end-to-end QoS. D. Priority Each connection l in the network is assigned a priority based on the experienced channel and delay within a time slot. The priority function φl of a connection l is an increasing function of channel quality and a decreasing function of d. III. J OINT BS A SSIGNMENT AND E ND - TO -E ND S CHEDULING A LGORITHM In this section, we adapt the end-to-end scheduling algorithm proposed in [9] to cope with heterogeneous services. Moreover, jointly with scheduling we propose an adaptive BS assignment algorithm that accounts for the pairs of BSs serving each uplink and downlink MS in an end-to-end connection. The resulting algorithm is summarized in Algorithm 1. A. BS Assignment Stage In a cellular network, a MS i possesses an active set Ai composed of M BSs that are candidate to serve it depending on the channel quality between the MS and each one of these BSs. Typically, the MS is assigned to the BS, out of its active set, having the best path loss. However, such a path loss based allocation can be inefficient in many scenarios. For this reason, other factors such as the BS load are important to be considered for BS assignment as in [3], [5], [6], [10] and [11]. In end-to-end scheduling, for every connection l between uplink MS i and downlink MS j, the BS assignment problem must be studied for the uplink and downlink. The first phase of
Algorithm 1 Proposed joint BS assignment and end-to-end scheduling algorithm per time slot. for l = 1 to K {Loop through all connections, each connection l has an uplink user i sending packets to downlink user j} do Stage 1. BS Assignment stage. Assign the uplink user i to the best BS in the active set based on path loss and load. Assign the downlink user j to the best BS in the active set based on path loss and load. end for for l = 1 to K {Loop through all connections, each connection l has an uplink user i sending packets to downlink user j} do Stage 2. Prioritization stage. Compute priority and debt for all connections. end for Connections Sorting. Sort connections by decreasing priority order for l = 1 to K {Loop through connections which were sorted by priority} do Stage 3. Debt sign inspection. if δl > 0 then Debt is positive, share the debt fairly between uplink and downlink in order to achieve fair contributions to the end-to-end utility debt between the two transmission directions. else Debt is negative or zero, scheduler connection with minimum allowable FSR. end if Stage 4. Power allocation. Compute uplink and downlink powers Pi,ci and Pj,cj for connection l. The power values are acceptable, if they satisfy the maximum power constraints for uplink and downlink in (13). end for
the proposed joint BS assignment and end-to-end scheduling algorithm is to go through all connections in the network, and assign their uplink and downlink MSs to the best serving BS based on path loss as well as the BS load. For every candidate BS c ∈ Ai of a MS i, we define the BS selection criterion χi,c which is an increasing function of the path loss gi,c and a decreasing function of the BS load. A MS i is assigned to the BS ci ∈ Ai which provides the highest value of the BS selection criterion χi,c . Subsequently, in this BS assignment phase of the algorithm, the following steps are executed for each connection l: 1) For the uplink MS i of connection l, compute the value of the BS selection criterion χi,c ∀c ∈ Ai for all the candidate BS in the active set of this MS. 2) Assign the uplink MS i to the uplink BS ci which provides the highest value of χi,c . 3) Repeat steps 1 and 2 for the downlink MS j of the connection. Consequently, this downlink MS j is served by the downlink BS cj which provides, within the downlink active set of MS j, the best BS selection criterion in the downlink. At the end of this stage, the users of all the connections in the network are assigned to the BSs which provide the best combination between path loss and BS load. Following BS assignment, the prioritization stage takes place. In this stage, the scheduler proceeds connection by connection and computes the values of the priority and debt. The output of prioritization is a prioritized listing of all packets with their respective debt value. The priorities are then used by the scheduler in the next two stages.
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B. Debt Sharing Stage In this phase, the scheduler inspects the sign of the debt δl for each connection l between uplink MS i and downlink MS j. When δl > 0, the scheduler fairly shares this positive debt between the uplink and the downlink MSs of the connection by taking into account the channel conditions of each direction, as performed in [9]. A “contribution” utility is defined for every MS and is a function of the debt share as well as the MS’s wealth (i.e. channel condition). The contribution utilities reflect the “real” contribution in terms of utility for every direction; allowing the scheduler to enable some sort of uplink/downlink collaboration for ensuring end-to-end utility. We define ρ and β = 1 − ρ as the fractions of the whole debt δl paid by the uplink and downlink respectively. The “contribution” utilities are denoted by hi (ρ) for the uplink and oj (β) for the downlink and represent decreasing functions of channel quality and increasing functions of the debt share. For allowing a fair debt share between the uplink and downlink users, we must have [9] (9) hi (ρ) = oj (β) Solving (9) yields the share of the debts for each direction. Subsequently, powers are allocated to connection l by solving the following equations deduced out of (6) and (8) for the uplink vi ≥ v˘i + ρ.δl (10) ˘j + β.δl for the downlink wj ≥ w ˘j are the minimum allowable utilities for the where v˘i and w uplink and downlink, respectively. Finally, through (8), it can be noted that if δl ≤ 0 then the connection in this time slot is able to achieve its utility target with minimum allowable uplink and downlink utilities with no debt sharing. C. Power Allocation Stage In this stage, the scheduler computes the powers for the uplink and the downlink of a connection l. The powers allocated for the the uplink and downlink MSs i and j of connection l are given by [9] gi,ci Pi,ci ≥
˜ i,c Γ i Si,s
(PR (α + 1) + σ 2 )
(11) ˜ Γ i (1 + Si,c ) i,s ˜ i,c is a target SIR value for the uplink MS resulting where Γ i Kci from (10), PR = k=1 gk,ci Pk,ci is the total received power at the uplink BS ci and Kci is the number of users assigned to BS ci that have been scheduled prior to and including the user i of the considered connection l. Pj,cj ≥
˜ j,c Γ j Sj,s
(gj,cj Pcj (λ + αj ) + σ 2 )
(12) ˜ j,c λΓ gj,cj (1 + Sj,s j ) where γ˜j,cj is a target SIR value for the downlink MS resulting from (10) and Pcj is the total transmit power of BS cj for the connections that have been scheduled prior to and including user j of connection l. The maximum uplink MS transmit power PM S and the maximum downlink BS transmit power PBS are accounted for as follows 0 < Pi,ci ≤ PM S 0 < Pcj ≤ PBS (13)
Furthermore, the computation of the uplink total received power PR and the downlink total transmitted power Pcj is given in [9]. Acceptable values of PR and Pcj are substituted for all the already scheduled connections for testing whether scheduling l yields a disconnection for any previously scheduled connection due to violation of constraints (13). If no other connection is affected, l is granted transmission, otherwise l is not selected since scheduling it yields a disconnection for connections with higher priority. IV. S IMULATION R ESULTS AND A NALYSIS A. Proposed Expressions For the transmission of a packet of length Ls in connection l between uplink MS i and downlink MS j, the priority, utility and contribution utility are given by gj,cj gi,ci g ¯ci · g ¯cj (14) φl = 3d e
1 √ 0.5di +1 vi (Γi , di ) = (1 − Q( 2Γi ))L s ·e 1 0.5dj +1 wj (γj , dj ) = (1 − Q( 2γj ))L s ·e
⎧ ⎪ ⎨ hi (ρ) = ⎪ ⎩ oj (β) =
ρ
gi,c i g ¯c i
β
gj,c
j
g ¯c j
(15)
for the uplink MS i =
(1−ρ) gj,c
j
for the downlink MS j
(16)
g ¯c j
where g¯ci and g¯cj represent the average pathloss for the uplink and the downlink, respectively. For a BS serving MSs belonging to a single service class s, the BS selection criterion which accounts for channel and BS load in the uplink or downlink for an MS i of service class s is given by gi,c (17) χi,c = ¯ Kc,s ¯ c,s is the BS load quantified as the number of active where K connections belonging to service class s, served by BS c and averaged over all the previous time slots and gi,c is the path loss between MS i and BS c. In the presence of multiple service classes under the coverage area of the same BS, (17) can be adapted by weighing the average load of each service class according to the QoS demands as will be seen in (18).
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TABLE I S IMULATION PARAMETERS . Number of cells and BSs C 7 Number of users 420 yielding 210 connections Time slot duration θ 10 ms Velocity of users 120 km/h FSR Target for uplink and downlink 0.999 FSR Margin ε for uplink and downlink 0.04 Chip rate 3.84 Mcps Path loss constant κ 125 dB Path loss exponent μ 4 Shadowing standard deviation σs 8 dB Number of BSs in active set M 3 Gaussian noise -133dbW Maximum UL transmit power PM S 150 mW UL intercell to intracell factor α 0.5 Maximum DL transmit power PBS 20 W DL average intercell to intracell factor α 0.8 DL orthogonality factor 0.4 Simulation total duration 30 seconds
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Fig. 1. Active connections vs. degree of non uniformity.
B. Results and Analysis The set of fixed parameters describing the simulated cellular network are summarized in Table I. In a first scenario, we consider all connections belonging to one service class named “Service 1” having a SF of 64, a target delay of τ1 = 80 ms, and FSR requirements as per Table I. Service 1 represents a delay sensitive service which has average requirements in terms of throughput (i.e. SF 64) such as a voice service or an end-to-end multimedia sharing session. Figure 1 presents the average number of active connections (selected to transmit) in a time slot as the degree of non uniformity increases (i.e. the fraction of the users that are located in the central cell at the start of the simulation). This figure shows that a highly non uniform network scenario yields a decrease in the average number of active connections due to the increased interference in the central cell. Figure 1 also shows that having a joint BS assignment scheme along with end-to-end scheduling results in significant gains in terms of active connections especially as the degree of user non uniformity increases. Further simulations are run for two network scenarios with heterogeneous services, one with 5/7 of the users in the central cell and the other one with 7/7 of the users (i.e. all the users) in the central cell. Two service classes are assumed: Service 1 previously mentioned and Service 2 which represents a delay tolerant service with high throughput requirements (e.g. file sharing or some type of mobile gaming). Service 2 is characterized by a SF of 16, a delay requirement of τ2 = 150 ms, and FSR requirements as per Table I. In order to account for this highly resource demanding service while assigning MSs to BSs, the BS selection criterion of (17) is modified as follows: gi,c (18) χi,c = S ¯ ¯ c,2 Kc,1 + ( Si,1 )·K i,2 ¯ c,1 and K ¯ c,2 represent the BS load quantified as where K the number of active connections belonging to Service 1 and Service 2, respectively. This new expression given by (18), gives a higher weight for the active Service 2 connections, since they are more resource demanding due to the lower SF. Therefore, a BS that has a high load of Service 2 connections is given a lower priority to be selected than a BS having a high load of Service 1 connections.
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Fig. 2. Active connections vs. percentage of Service 2 connections.
Fig. 3. Total packet drop ratio vs. percentage of Service 2 connections.
Figure 2 presents the average number of active connections as a function of the percentage of Service 2 connections. Results indicate that using joint scheduling and BS assignment yields significant gains in terms of the number of active connections for Service 1. In addition, as the percentage of Service 2 connections increases, the BS assignment gains of Service 1 connections are reduced due to the availability of a lower number of active Service 1 connections. For the 7/7 case, the highest gains in terms of active Service 1 connections are achieved at 0% and 20% of Service 2 connections. At this network distribution, using BS assignment yields around 75% improvement at 0% Service 2 connections and 70% improvement at 20% Service 2 connections. With regards to Service 2, we note that for the non-uniform case of 5/7, no Service 2 gains in active connections exist. However, for the non-uniform case of 7/7, we notice an improvement up to 100% more connections at 80% and 100% Service 2 connections. The total packet drop ratio achieved by the two services for the different network distributions is shown in Figure 3. This figure shows that as a result of the high resource demands of Service 2, the packet drop ratio for connections belonging to this service increases as the percentage of Service 2 connections increases. Moreover, with the increase in the number of Service 2 connections, the drop of Service 1 connections decreases due to the opportunistic nature of the proposed algorithm. Figure 3 presents a significant advantage for having BS assignment in terms of Service 1 packet drop for both 5/7 and 7/7 cases. ACKNOWLEDGEMENTS
show that a joint BS assignment scheme which accounts for the BS load, while assigning the uplink and downlink users of an end-to-end connection to their serving BSs, can significantly improve the performance in terms of higher average number of active connections and lower packet drop ratio.
This work was partially supported by the Lebanese American University (LAU) research council. V. C ONCLUSIONS In this work, we proposed a joint BS assignment and endto-end scheduling algorithm that provides end-to-end quality guarantees. The end-to-end scheduler was evaluated in various network scenarios for homogeneous and heterogeneous services with a uniform and non-uniform MS distribution. We
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