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Optimal Call Admission Control with QoS Guarantee in a Voice/Data Integrated Cellular Network Tat-Chung Chau, K. Y. Michael Wong, and Bo Li
Abstract— This paper addresses the issue of call admission control with the necessary Quality-of-Service (QoS) guarantee for an integrated service mobile cellular network. Specifically, we extend the Limited Fractional Guarded Channel (LFGC) scheme to incorporate the multiple traffic types, and derive the set of parameters that leads to the optimal call admission control. The key challenges are the state-dependent nature of the admission control, and the increasing complexity of the state space in a multi-services environment. We propose a novel control meachanism that only uses a few parameters (2-5) to characterize the optimal control planes, and use the simulated annealing technique to obtain the optimal control parameters. Index Terms— Guarded channel, call admission control, wireless networks.
I. I NTRODUCTION HERE has been a rapid development and deployment in wireless cellular communications. The next generation of networks are expected to eventually carry multimedia traffic - combinations of voice, video, images, or data. One of the key issues is to ensure that the QoS requirement of different applications are guaranteed. This paper addresses the call admission control for a voice/data integrated wireless cellular network. When a mobile subscriber moves across the boundary of a cell, handoff dropping can occur. This is primarily caused by the unavailability of channels in the new cell. With cell sizes being systematically decreased to enable better frequency reuse (e.g., the use of micro-cells or pico-cells), the capacity of the overall system increases, but the number of handoffs during a mobile call’s lifetime also increases considerably. Therefore, it becomes increasingly critical in micro or pico-cell wireless
T
Manuscript received July 19, 2004; revised January 30, 2005; accepted March 23, 2005. The associate editor coordinating the review of this letter and approving it for publication was Z. Zhang. This work was supported in part by grants from Research Grants Council (RGC) under contracts HKUST6153/01P, HKUST6062/02P, HKUST6204/03E, HKUST6104/04E, and HKUST6165/05E, by a grant from NSFC/RGC under the contract NHKUST605/02, and by grants from National NSF China under the contracts 60429202 and 60573115. We acknowlege Y. Keung for a careful reading of the manuscript. During the proofreading stage of this paper an alternative statistical approach to the 2-parameter DT-CAC policy, applicable to cells of arbitrarily large capacities, has become available in the following reference: Y. Keung, MPhil thesis, HKUST, 2004. T.-C. Chau and K. Y. M. Wong are with the Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. B. Li is with the Computer Science Department, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (e-mail:
[email protected]). Digital Object Identifier 10.1109/TWC.2006.05021.
networks to have necessary control mechanisms that meet the following two challenges. First, dropping a call in progress is more undesirable to the users than rejecting (blocking) a newly requested call. Therefore, one of the key design goals is to maintain the handoff dropping probability at pre-specified target QoS levels, independent of the traffic conditions in the system [1]. Second, in view of the increasing popularity of data services from simple short messages to General Packet Radio Service (GPRS), there also arises a need for data service to be guaranteed, and the network must satisfy the different QoS requirements of all types of traffic. This imposes more stringent QoS requirements of individual calls, mandating a highly precise resource allocation [24]. One of the new challenges in a multi-service network is that the wireless resource is shared among multiple traffic types. This can usually be done by Complete Sharing (CS), Complete Partitioning (CP) or their hybrids [3], [6], [18]. The CP approach divides the available channels into separate subpools dedicated to each type of traffic. However, a simple mathematical derivation would demonstrate that a CS scheme can produce better channel efficiency [16]. Hence to maximize channel utilization, we adopt the CS approach, which allows all types of traffic to access all available channels at all times, yielding a higher efficiency in resource utilization. Specifically, based on a model we developed in [16], we propose a Dual-Threshold Call Admission Control (DT-CAC) policy; we formulate the optimal call admission control problem whose objective is to minimize the maximum new call blocking probability (voice or data) while satisfying the hard constraints on handoff dropping probabilities for both voice and data traffic. The main complication is that the call admission control becomes a state-dependent decision. Since the state space becomes increasingly complex for multiple classes, specifying the control action at each location in the state space becomes prohibitively complex. It is prudent to summarize the control policy using relatively few parameters, which characterize the thresholding surfaces in the state space cutting off either the voice or data new calls. These are conveniently approximated by sets of planes, as illustrated in this paper. Even with this simplification, we have to search for the optimal control policy in a space with 2 to 5 dimensions of continuous parameters. Already, this is a prohibitively complex task for exhaustive search. Therefore, we have to use an effective algorithm to find out the parameter setting.
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Another price that we pay for this simplification is that the monotonic behavior of the cost functions, commonly exhibited in other schemes [16], [21], no longer holds. Thus methods such as gradient descent or bisection are not applicable. It is necessary to use an efficient and reliable technique of complex optimization which is not plagued by the presence of multiple local minima. The simulated annealing (SA) method becomes the natural candidate in obtaining the optimal threshold values. The rest of the paper is organized as follows. We review some of the existing work in Section 2. The DT-CAC policy and its performance calculations are presented in Section 3. The dual thresholds and their optimal selection are discussed in Sections 4 and 5 respectively. Numerical results and analyses are given in Section 6. Section 7 concludes the paper with discussions on future work. II. T HE E XISTING S CHEMES The Guarded Channel (GC) based policies have been extensively studied in the traditional voice-centric wireless cellular networks [10], [19]. The basic idea is to reserve a number of channels exclusively for handoff calls in each cell by introducing a threshold T in each cell, where T is an integer between 0 and the cell capacity C. When a new call arrives at a cell, the system accepts the new call only if the number of ongoing calls in the cell is less than T , otherwise the call will be blocked. Handoff calls will be dropped by the system only when no channels are available in the cell. So the control policy reserves C − T channels for handoff calls. In order to meet the target call dropping probability PQoS , we can choose a T such that the system call dropping probability PDrop ≤ PQoS . The trade-off is that the increase in the number of channels reserved for handoff will lower the PDrop , but causing the new call blocking probability PBlock to rise. The common practice is to choose a T that makes PDrop as close to the target PQoS as possible while obtaining the minimum PBlock . Ramjee et al in [21] derived optimal admission control policies for three problems: minimizing a linear objective function of the new and handoff blocking probabilities (MINOBJ), minimizing the new call blocking probability with a hard constraint on the handoff call blocking probability (MINBLOK), and minimizing the number of channels used with hard constraints on both new and handoff call blocking probabilities (MINC). It was demonstrated that the wellknown GC scheme is optimal for the MINOBJ problem, while the newly proposed Fractional Guarded Channel (FGC) policies are optimal for the MINBLOCK and MINC problems. The FGC policy can reserve a non-integral number of guarded channels for handoff calls. The basic idea is to allow the value of the threshold to be a real number, which has an integer part T , and a fractional part α. When the state is equal to T , new arrival calls will be accepted with probability α. The value of the threshold T + α can be obtained by bisection method with the constraint PDrop = PQoS . For networks accommodating both narrow-band and wideband traffic, two-tier resource allocation schemes were investigated [3], [6]. Two types of traffics were considered, namely narrow-band (NB) and wide-band (WB) with bandwidth consumption at one unit and M units, respectively. It
was further assumed that only NB traffic handoff is considered. The objective is to maximize the bandwidth utilization while ensuring that NB traffic is not dropped during handoff and new users assured access to the system. The relative prioritization of the different users is given by the relative blocking/dropping probabilities. The results demonstrated that the CS scheme can obtain high bandwidth utilization at the expense of providing only single fixed QoS profile, which does not offer any guarantee for handoff traffic. In addition, the CS scheme also favors NB users over the WB users. On the other hand, it was shown that CP can provide guarantee to the respective QoS specified by each traffic type, at the expense of system utilization. The results showed that with proper dimensioning, better overall performance can be obtained by hybrid reservation schemes. Haung et al proposed a bandwidth allocation scheme for a voice/data integrated system [11], where bandwidths assigned to voice and data are separated. Its unique feature is that the boundary for the partition is “movable”, thus can effectively deal with the traffic changes in the system. Specifically, among the channels in each cell, those in the voice-only-area or data-only-area are reserved exclusively for voice or data respectively. The remaining channels (shared-area) are fairly shared by both calls. Calls are firstly directed to their restricted service areas only before competing for the shared area. GC policy can be further implemented within each specific service area to provide the needed QoS guarantee. Li et al proposed a hybrid cutoff priority scheme for wireless cellular networks [14]. It can support an arbitrary number of traffic types, each having different QoS requirements in a wide variety of parameters, such as the number of channels needed, the call holding time and the cutoff priority. The formulation provides a general framework for bandwidth provisioning for multiple types of traffic, but given the computation complexity, performance results were obtained from the stochastic Petrinet approximation. Chen et al proposed a general multiple threshold bandwidth reservation scheme [4]. The proposed scheme can handle multiple types of traffic, one of the key issues discussed is the fairness among different traffic streams. It defined a fariness index by incorporating the pre-specified weight of each traffic and the current traffic loading. It, however, does not address the issue of optimal threshold selection. III. T HE C ALL A DMISSION C ONTROL P OLICY In this section, we present the Dual-Threshold Call Admission Control (DT-CAC) policy. Both voice and data traffic are considered, where the data traffic refers to all information encoded as data streams which consume more bandwidth than the voice traffic. The proposed DT-CAC policy builds upon the Limited Fractional Guard Channel (LFGC) scheme used in a voice-only cellular network [21]. As proposed by Ramjee et al [21], the LFGC scheme provides accurate guarantees for target QoS such as the handoff dropping probability. The idea is to allow the value of the threshold to be a real number which has an integer part T and a fractional part α. When there are less than T calls in the cell, the system will accept all calls. When there are more than T calls, only handoff calls will be allowed. When there are T calls, new arrival calls will
CHAU et al.: OPTIMAL CALL ADMISSION CONTROL WITH QOS GUARANTEE IN A VOICE/DATA INTEGRATED CELLULAR NETWORK
be accepted with probability α. Assume that the call arrival rates, the average call duration and cell residence times, and the cell capacity are constant. The probability Pn that there are n active calls in the cell can be obtained by solving the one-dimensional Markov chain [12]. The dropping probability PDrop and the blocking probability PBlock are then obtained C from PDrop = PC and PBlock = (1 − α)PT + j=T +1 Pj , where C is the cell capacity. The value of the threshold T + α can be obtained by equating PDrop to the probability PQoS required by the QoS constraint. Numerically, this can be solved by the bisection method.
determine the call admission depending on traffic types and system loading: •
•
A. The Basic Mechanism We consider a cellular network of close packed hexagonal cells using a fixed channel allocation scheme. To alleviate finite size effects, the network is connected periodically on the periphery. The system deals with two types of traffic: voice and data with bandwidth requirements of 1 and B channels respectively. The performance parameters are: (1) The call blocking probability for voice Pbv ; (2) The call dropping probability for voice Pdv ; (3) The guaranteed QoS for voice PQoSv in terms of a target voice handoff dropping probability; (4) The call blocking probability for data Pbd ; (5) The call dropping probability for data Pdd ; (6) The guaranteed QoS for data PQoSd in terms of a target data handoff dropping probability. The proposed policy is a state-dependent approach. The state of a cell is described by the number of ongoing voice and data calls in it, denoted by m and n respectively. Hence, in the two-dimensional space of non-negative integers m and n, a possible state of the cell corresponds to a point (m, n) bounded by the inequality m+Bn ≤ C in a triangular region. We consider control policies which can take four possible actions on new calls, depending on the state location in this triangular region: (a) accepting both voice and data new calls; (b) accepting only voice new calls; (c) accepting only data new calls; (d) rejecting both voice and data new calls. On the other hand, the control policy accepts all handoff voice and data calls as far as the cell capacity allows. It is reasonable to expect that in smooth control policies, the four regions of increasingly restrictive controls should be contiguous to each other. Hence, it is sufficient to describe the control policy by the surfaces demarcating the four regions in the state space. In the case of two-class traffic, the dividing surfaces correspond to two (possibly intersecting) curves, one being the threshold for new voice calls, the other for new data calls. Finding the optimal curves could be an extremely complex task. It is therefore practical to characterize the curves by relatively few parameters, and restrict the search for the optimal control policy to this simplified parameter space. To ensure a smooth variation of the control function, we allow the parameters to take continuous values. This can be considered as the two-dimensional extension of the LFGC policy. Hence the proposed CAC policy is based on a dualthreshold approach. For each cell, two thresholds are used. The threshold for voice calls is defined by the curve m = Tv (n), and the threshold for data calls is n = Td (m). Upon each new call arrival, the following mechanism is used to
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For each new voice arrival, the system will accept the call if there is at least one available channel and m < Tv (n), and will accept the call with probability frac(Tv (n)) if there is one available channel and m = Tvoice (where x and frac(x) mean the integer and fraction parts of x respectively). Otherwise, the call will be blocked. For each new data arrival, the system will accept the call if there is at least B channels available and n < Td (m), and will accept the call with probability frac(Td (m)) if there are B channels available and n = Td (m). Otherwise, the call will be blocked. For a voice or data handoff call, it is accepted whenever there is one or B available channels for voice and data arrival respectively. Otherwise, the call will be dropped.
B. The Queuing Model A queuing model can be developed to obtain the performance index in terms of call blocking probabilities and handoff dropping probabilities for both types of traffic. We assume that new calls arrive according to Poisson distributions with arrival rates λnv for voice and λnd for data, handoff calls arrive according to Poisson distributions with the arrival rates λhv for voice handoff and λhd for data handoff. We further assume that the call duration time are exponentially distributed with averages 1/μv and 1/μd respectively (i.e., connected calls terminate at the rates of μv and μd respectively), and the cell residence times are exponentially distributed, with averages 1/hv and 1/hd respectively. This set of assumptions has been found to be reasonable as long as the number of mobile users in a cell is much greater than the number of channels, which is particularly true for micro- or pico-cell systems, and it has been widely used in the literature. 1 The handoff arrival rates λhv and λhd , for voice and data respectively, cannot be explicitly assigned. They are dependent on the other parameters. Using the mean-field approximation in the case where the traffic in each cell is identically distributed, they can be expressed in terms of the average number of ongoing voice and data calls in the nearest neighboring cells, λhv = mhv ; λhd = nhd , where m and n denote the average occupancies of a cell, and have to be obtained self-consistently as described below. The actual call arrival rate in a cell depends on the control policy it is adopting. The total call arrival rate λtv (m, n) for voice calls is given by (a) λhv + λnv if 0 ≤ m ≤ Tv (n), (b) λhv + frac(Tv (n))λnv if m = Tv (n), (c) λhv if Tv (n) < m < C, (d) 0 if otherwise. Similarly, the total call arrival rate λtd for data calls is given by (a) λhd + λnd if 0 ≤ n ≤ Td (m), (b) λhd + frac(Td (m))λnd if n = Td (m), (c) λhd if Tv (m) < n < C/B, (d) 0 if otherwise. We can derive the steady-state probabilities Pm,n of having m voice and n data calls ongoing in a cell. The steady-state 1 Noticeably, however, the cell residence time does not necessarily obey the exponential assumption [8]. A necessary and sufficient condition for this to be held was given in [7].
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balance equations for states inside the boundaries of the state space are given by
(a)
C/B
Threshold for voice calls Threshold for data calls
C/B
(b)
[λtv (m, n) + λtd (m, n) + mμv + nμd ]Pm,n = (m + 1)μv Pm+1,n + (n + 1)μd Pm,n+1 + λtv (m − 1, n)Pm−1,n (1)
The balance equation along the boundary of the state space can be written down in a similar way, by excluding those terms in Eq. (1) not allowed by the boundary. Together with the normalization condition m,n Pm,n = 1, we can then obtain a set of linear independent equations which can be solved directly by LU decomposition [20]. We can now determine the average occupancies appearing in the expressions of the handoff arrival rates, using m = m,n mPm,n ; n = m,n nPm,n . However, the state probabilities Pm,n in turn depend on m and n via the handoff arrival rates. Therefore, their self-consistent solutions have to be found by iteration. The values of the call blocking and dropping probabilities can then be calculated, Pm,n , Pdd = Pm,n , (2) Pdv =
number of data calls
+ λtd (m, n − 1)Pm,n−1 .
θ pd C/B bv
pv
p1
C (c)
p2
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C/B b2 b1
bd
θ ad av C number of voice calls
a1 a2
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Fig. 1. (a) The 2-parameter approach, the (b) 3-parameter approach , (c) the 4-parameter approach , (d) the 5-parameter approach.
data calls will be rejected. Thus the control policy consists of three, instead of four, regions. When pv > pd , the region of rejecting only new voice calls is absent, whereas for pv < pd , there is no region of rejecting only new data calls. 2) The 3-parameter Characterization: A natural extension m+nB=C m+nB>C−B of the 2-parameter scheme is to restore the possibility of all the four possible regions in the state space. This can be done Pm,n + Pm,n [1−frac(Tv (n))], Pbv = by partitioning the region between the two thresholding planes n; m>Tv (n) n; m=Tv (n) (3) into two regions, each rejecting only new voice or data calls, as shown in Fig. 1(b). To maintain a fair distribution of voice Pbd = Pm,n and data calls, only new voice calls are rejected in the region m; n>Td (m) with ongoing calls dominated by ongoing voice calls, and only + Pm,n [1 − frac(Td (m))]. (4) new data calls are rejected in the other region. This creates the m; n=Td (m) tendency to push the state of the system back to the vicinity of the partition whenever it starts to deviate to either side. IV. T HE D UAL T HRESHOLDS Specifically, the three parameters p1 , p2 and θ characterize Our objective is to determine the set of thresholds Tv the three boundaries in Fig. 1(b) via the equations m + Bn = and Td that can minimize the maximal new call blocking p1 , m + Bn = p2 and n = m tan θ. The state space is divided probability, i.e., minTv ,Td max(Pbv , Pbd ), while satisfying the into 4 regions. When m + Bn ≤ p1 , all calls are accepted. hard constraints on the handoff dropping probabilities for When p1 < m + Bn ≤ p2 , either voice or data arriving calls both voice and data traffic. This turns out to be particularly are blocked, depending on whether the ratio n/m of ongoing challenging, and the complications are primarily caused by data and voice calls is respectively less than or greater than the two factors: 1) the complete sharing nature of the DT-CAC ratio threshold tan θ. This results in zig-zag shaped thresholds scheme, in which the monotonic behavior exhibited in other for both voice and data calls, as illustrated in Fig. 1(b). The optimal search is made in the ranges 0 < p1 ≤ p2 ≤ schemes does not work, thus numerical methods such as the bisection method are not applicable; 2) given the continuous C + 2 and 0 ≤ θ ≤ π/2. We note in passing that the 2nature of the thresholds (Tv and Td ), it is impossible to parameter approach can be considered as a subset of the 3use an exhaustive approach to search for the optimal values. parameter one. When the angle of inclination θ of the partition In this section, we first propose four characterizations of in between the thresholding planes is 0, the control policy the thresholds, which will be optimized by the simulated reduces to one without the region of rejecting only new voice calls. On the other hand, when θ becomes π/2, the region of annealing techniques described in the following section. 1) The 2-parameter Characterization: Figure 1(a) shows the rejecting only new data calls is absent. However, unlike the 2characterization of two thresholds pv and pd , which can be any parameter approach in which the thresholds for new voice and real numbers between 0 and C+2. The reason of allowing both data calls are straight lines, here the thresholds are zig-zags. points to go beyond the cell capacity C is to allow the system 3) The 4-parameter Characterization: To avoid the zigto have an opportunity to fully utilize bandwidth under light zag thresholds, we consider the 4-parameter approach which traffic conditions. In the state space of m and n respectively is generalized from the 2-parameter one by allowing the slopes representing the number of ongoing voice and data calls, the of the lines to vary. To characterize each threshold, we let av threshold Tv follows m + Bn = pv . In the states above this and bv be the m- and n-intercepts of the linear voice threshold line, new voice calls will be rejected. Similarly, the threshold respectively, and ad and bd be the m- and n-intercepts of the Td follows m + Bn = pd . In the states above this line, new linear data threshold respectively, as shown in Fig. 1(c). Since
CHAU et al.: OPTIMAL CALL ADMISSION CONTROL WITH QOS GUARANTEE IN A VOICE/DATA INTEGRATED CELLULAR NETWORK
Cost function vs.θ Fixed p1 and p2 0.9
Cost function
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Fig. 2.
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Cost function against θ for the 3-parameter case.
the slopes of the thresholding lines can be varied, the policy can work with either only three regions if the two lines do not cross, or with four regions if otherwise. The constraints in the optimal search are: 0 < bv , bd < (C + 2)/B, and 0 < av , ad < C. The thresholds Tv and Td can be described respectively by m/av + n/bv = 1, m/ad + n/bd = 1. 4) The 5-parameter Characterization: The 5-parameter approach can be obtained from the 4-parameter approach by adding an angular parameter θ similar to the 3-parameter approach. The thresholds in this approach also has the zig-zag shape as shown in Fig. 1(d). The constraints of the parameters in the optimal search are: 0 < b1 < b2 < (C + 2)/B, 0 < a1 < a2 < C + 2, and 0 < θ < π/2. V. T HE O PTIMIZATION OF THE PARAMETERS To ensure fairness of resource allocation to both classes of traffic, the cost function E(x) to be minimized (also called the energy function) is the maximum of the call blocking probabilities of both traffic classes, subject to the constraints that the call dropping probabilities are bounded by the QoS requirements, namely, minimize E(x) subject to Pdv and Pdd
≡ max(Pbv , Pbd ), ≤ PQoSv
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value of θ corresponds to a policy dominated by cutting off new data arrivals inside the region bounded by the thresholding lines, and the other dominantly cuts off new voice arrivals. The existence of multiple local minima implies that ordinary optimization techniques such as gradient descent may get trapped before the system reaches the global minimum. Hence, we resort to simulated annealing to circumvent the difficulty. Simulated Annealing (SA) is a commonly used algorithm for optimization problems [13], when multiple local minima are possibly found in the landscape of the cost function. One starts the system with a random configuration at a very high fictitious temperature, and then reduces the temperature very slowly until it reaches the desired temperature. This allows the system to jump out of local minima, and consequently, arrive at configurations close to the global minimum. If the temperature can be reduced at a sufficiently slow rate, it is possible to obtain the optimal solution. However, if the temperature is reduced too slowly, it renders the method impractical. Geman et al [9] showed that the optimal value is guaranteed found if the temperature is reduced in n steps as Tn = T0 / ln n, where T0 is the initial temperature. In practice, faster annealing schedules are implemented but still maintains satisfactory convergence. For example, in this paper we assign the temperature Tk at the k th epoch according to the power-law schedule: Tk = T0 /k, where each epoch consists of sufficient Monte Carlo steps for thermal equilibration. The procedures used to derive the minimum of the maximum call blocking probability E(x) are listed in Table 1. Compared with the original SA algorithm, we have added the hard constraint for the QoS requirement in step 3, and only keep track of the state with the lowest energy, rather than finding its thermal average. We perform simulations on a hexagonal cluster of 19 cells with capacity C = 30. In our simulations, we measure the value of energy every 10 Monte Carlo steps, and the average value of energy for 20 successive measurements is then calculated. At relatively high temperatures the system can reach thermal equilibrium as fast as 600 Monte Carlo steps, while it takes over 1500 Monte Carlo steps at low temperature. Each simulation is performed for network traffic time of 172,800 s (2 days). To eliminate statistical fluctuations, the dropping and blocking probabilities are averaged over 10 simulations. VI. R ESULTS
(5)
≤ PQoSd ,
where x is a state in the phase space. An alternative definition of the cost function is a linear combination of the mean and standard deviation of the call blocking probabilities of both classes [6]. We note that the maximum√of two quantities can be obtained by adding their mean and 2 times the standard deviation. Hence we expect that the present definition of the cost function is representative of a family of functions. Nevertheless, the method of simulated annealing can be applied to various definitions of the function. Figure 2 illustrates the existence of local minima in the problem. It shows two local minima; the one with a lower
As shown in Fig. 2, the presence of the barrier surrounding the local minima shows that the SA algorithm is necessary. Also from Fig. 2, we set the initial temperature at the order of the depth of the minimum, and the initial step size of the angular parameter θ set at 20 degrees, since it allows the system to jump from one minimum to another in finite number of steps. We found that it is sufficient to use 10 epochs to obtain the value of parameters that yield excellent control. Below, we present the results for several cases. 1) Network Condition 1 (Benchmark): The benchmark simulations are based on the following typical parameters: B = 2, μv = 0.005s−1 , μd = 0.01s−1 , hv = 0.01s−1 , hd = 0.005s−1, λnv : λnd = 2 : 1, PQoSv = 0.01, PQoSd = 0.05.
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TABLE I S IMULATED ANNEALING PROCEDURE TO FIND THE MINIMUM E(x). 1 2 3 4 5
6 7
Set the epoch number k to 1. Randomly choose a state x in the phase space as the initial state. Do while the minimum energy state is different from that of the previous epoch: Do while the system has not reached thermal equilirbrium: Move to a state x which is adjacent to state x with finite step size. If the Pvd or Pdd cannot meet the QoS requirement, go back to Step 3. If E(x ) ≤ E(x), accept the move if E(x ) ≤ E(x), Else accept the move with probability exp[−(E(x ) − E(x))/T ]. End if If the new E(x) is lower than the global minimum energy in the memory, store the new state x as the global minimum energy state y. End do Increase the epoch number by 1. Set the current state x to be the global minimum energy state y. Divide the initial values of the temperature and step size by k. End do Record the state y as the optimal result.
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Cost function
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2 parameters 3 parameters 4 parameters 5 parameters CP
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The cost function for network condition 1. Fig. 4. 1.
First, we compare the call blocking and dropping probabilities obtained from the theoretical queuing model and simulations for the 2-parameter approach. There is an exellent agreement between theory and simulations, showing the validity of the mean-field approximation on the average occupancies. Figure 3 compares the cost functions, which are the minimum of the maximum blocking probabilities, of the four proposed DT-CAC schemes based on 2, 3, 4, and 5-parameter approaches, and the CP scheme as well. It is interesting to note that the four proposed DT-CAC schemes yield similar performance. Compared with the DT-CAC schemes, the CP scheme consistently produces higher values of the cost function, indicating that the fixed partition between voice and data calls lead to inefficient utilization of the channels. This result implies that a higher utilization can be obtained by optimal thresholds in the framework of CS. As noted in [24], traditionally the dropping probabilities were not estimated precisely, leading to problems of overprovisioning or under-control. Hence we show the dropping probabilities of voice and data calls in Figs. 4 and 5 respectively. We can see that the four DT-CAC schemes yield similar
The dropping probability Pdv of voice calls for network condition
results. All of them can maintain dropping probabilities below the QoS requirements. However, the dropping probability of data calls is far below the targeted QoS requirement. This is a characteristic of the optimal solution, in which only one of the two inequalities is saturated, except for very carefully chosen constraint parameters. This arises from the need to minimize the maximum blocking probability, for otherwise, attempts to saturate both QoS constraints will generally lead to unequal blocking probabilities of voice and data calls, whose maximum can be possibly reduced by more equalized alternative solutions [2]. In contrast, the CP method which has a higher cost function, can saturate both QoS requirements. 2) Network Condition 2 (Change in QoS): Figures 6, 7 and 8 are based on the benchmark parameters except that where the QoS requirements are 10 times more stringent. Figure 6 shows the cost function value, that is, the minimum of the maximum blocking probability. Compared with the cost function value in Fig. 3, here the improvement of using the proposed DTCAC schemes over the CP scheme is even more significant.
CHAU et al.: OPTIMAL CALL ADMISSION CONTROL WITH QOS GUARANTEE IN A VOICE/DATA INTEGRATED CELLULAR NETWORK
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The dropping proability Pdd of data calls for network condition 1.
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The cost function for network condition 2.
Figures 7 and 8 show the dropping probabilities of voice and data calls respectively. Similar conclusion can be drawn from the graphs in that the four proposed DT-CAC schemes can all satisfy the QoS requirement. 3) Network Condition 3 (Changes in Bandwidth): Figures 9, 10 and 11 are based on the benchmark parameters, except that we increase the bandwidth required by data traffic to f ive channels. Since the resource available is tightened by the larger bandwidth requirement, the network saturates at a lower call rate. The minimum of the maximum blocking probability in Fig. 9 shows that the proposed DT-CAC schemes can maintain a high resource utilization by letting more traffic into the system than the CP scheme, analogous to the benchmark result. Comparing Figs. 10 and 11 with Figs. 4 and 5, we find that the control bottleneck in this case is the data traffic rather than the voice traffic. In network condition 1, the dropping probability of the data class is far below the QoS requirement, while the voice class saturates the QoS requirement. In the present network condition, the situation is reversed. 4) Network Condition 4 (Changes in Traffic Ratio): The simulations are based on the benchmark parameters, except
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Fig. 8. The dropping probability Pdd of data calls for network condition 2.
that the ratio of the voice and data call arrivals has been increased to 5 : 1, resulting in a higher proportion of voice traffic in the system. Again, the proposed DT-CAC schemes have a value much lower than the CP scheme, and all DT-CAC approaches can guarantee the QoS. VII. C ONCLUSION We have proposed a new call admission control policy called Dual-Threshold Call Admission Control (DT-CAC) policy, whose objective is to minimize the maximum new call blocking probability while satisfying the hard constraints on handoff dropping probabilities for both voice and data traffic. Using the Simulated Annealing technique, we obtain the optimal set of thresholds that can achieve the objective. The results are supported by simulation. We have also demonstrated the power of the Simulated Annealing algorithm. We anticipate when there are more than two classes of traffic, simulated annealing will be even more effective to find the optimal parameters in the high dimensional space, avoiding the inefficiency of an exhaustive search.
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It is instructive to compare the results of simulated annealing with exact solutions. However, when the number of parameters increases, exact solutions become increasingly intractable. Nevertheless, exhaustive search for the optimal solution is still feasible in the case of 2 parameters, where a comparison between simulated annealing and exhaustive search using similar step sizes of search shows that the found optimal solutions are similar. It is known that simulated annealing is associated with the “premature” problem, where the cost function stays at a local minimum for many iterations. This problem can be overcome by slow cooling schedules, and more stringent stopping criteria. The result is ultimately a compromise between the quality of the solution and the amount of computational resource available. In this paper, we have demonstrated that satisfactory performances can be obtained using moderate computational efforts. To our pleasant surprise, we find that the four DT-CAC schemes yield similar results, so that the optimal control
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Fig. 12. Distribution of states for (a) 2-parameter control, (b) 4-parameter control at the call arrival rate of 0.065 calls per second.
can be effectively described by two parameters only. To better understand the rationale, we investigate the probability distribution of states for each scheme. Figure 12 shows the probability distribution for two schemes at the same call arrival rate, where both cost functions are effectively the same, as shown in Fig. 3. We observe that the peaks of the distributions are all concentrated in a small area at almost the same location for the four methods. This is particularly encouraging, since we would like to limit the number of parameters when there are dramatically more traffic classes in future multimedia networks. More concrete confirmation of this feature is necessary.
CHAU et al.: OPTIMAL CALL ADMISSION CONTROL WITH QOS GUARANTEE IN A VOICE/DATA INTEGRATED CELLULAR NETWORK
A number of assumptions necessary for the mathematical derivations have been made in this paper, as is often the convention of most network analyses. However, they might not be entirely realistic. In particular, the data traffic does not necessarily obey the exponential distribution in both call duration time and channel holding time. Further investigations can be carried out by relaxing the exponential assumptions. Another avenue for future study is to use the pre-assignment strategy proposed in [18], as there are significant complexity involved in solving the corresponding Markov chain when using policies based on GC (referred to as a post-assignment scheme in [18]). Furthermore, a possible extension of the proposed scheme is its generalization to next-generation cellular networks, in which the cell capacity is characterized by powerlevel and interference instead of the number of channels. R EFERENCES [1] I. F. Akyildiz, J. McNair, J. Ho, H. Uzunalioglu, and W. Wang “Mobility management in next generation wireless systems,” Proc. IEEE, vol. 87, no. 8, pp. 1347-1384, Aug. 1999. [2] T. C. Chau, K. Y. M. Wong, and B. Li, “Optimizing call admission control with QoS guarantee in a voice/data integrated cellular network using simulated annealing,” in Proc. IEEE GLOBECOM, Nov. 2002. [3] J. Chen and M. Schwartz, “Reservation strategies for multi-media traffic in a wireless environment, performance summary,” in Proc. IEEE PIMRC’95. [4] X. Chen, B. Li, and Y.-G. Fang, “Dynamic multiple threshold bandwidth reservation (DMTBR) scheme for QoS provisioning in multimedia wireless networks,” to appear in IEEE Trans. Wireless Commun. [5] M. Cheng and L.-F. Chang, “Wireless dynamic channel assignment performance under packet data traffic,” IEEE J. Select. Areas Commun., vol. 17, no. 7, pp. 1257-1269, July 1999. [6] B. Epstein and M. Schwartz, “Reservation strategies for multi-media traffic in a wireless environment,” in Proc. IEEE Vehicular Technology Conference 1995. [7] Y. Fang, I. Chlamtac, and Y.-B. Lin, “Channel occupancy times and handoff rate for mobile computing and PCS networks,” IEEE Trans. Computers, vol. 47, no. 6, pp. 679-692, June 1998. [8] Y. Fang and I. Chlamtac, “Teletraffic analysis and mobility modeling of PCS networks,” IEEE J. Select. Areas Commun., vol. 17, no. 7, pp. 1062-1072, July 1999. [9] S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, Nov. 1984. [10] R. Guerin, “Queueing-blocking systems with two arrival streams and guarded channels,” IEEE Trans. Commun., vol. 36, no. 2, pp. 153-163, Feb. 1988. [11] Y.-R. Haung, Y. B. Lin, and J. M. Ho, “Performance analysis for voice/data integration on a finite-buffer mobile system,” IEEE Trans. Veh. Technol., vol. 49, no. 2, pp. 367-378, Feb. 2000. [12] B. R. K. Kashyap and M. L. Chaudhry, An Introduction to Queueing Theory. A and A Publications, 1988. [13] S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671-680, 1983. [14] B. Li, C. Lin, and S. Chanson, “Analysis of a hybrid cutoff priority scheme for multiple classes of traffic in multimedia wireless networks,” ACM/Baltzer J. Wireless Networks, vol. 4, no. 4, pp. 279-290, Aug. 1998. [15] B. Li, L. Yin, K. Y. M. Wong, and S. Wu, “An efficient and adaptive bandwidth allocation scheme for mobile wireless networks based on online local parameter estimations,” ACM/Kluwer J. Wireless Networks, vol. 7, no. 2, pp. 107-116, Mar./Apr. 2001. [16] B. Li, L.-Z. Li, B. Li, K. Sivalingam, and X.-R. Cao, “Call admission control for voice/data integrated cellular networks: performance analysis and comparative study,” IEEE J. Select. Areas Commun., vol. 22, no. 4, pp. 706-718, May 2004. [17] Y. B. Lin, “Performance modeling for mobile telephone networks,” IEEE Network, vol. 11, no. 6, pp. 63-67, Nov./Dec. 1997.
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[18] X. Luo, B. Li, I. Thng, Y.-B. Lin, and I. Chlamtac, “A measurementbased pre-assignment scheme with connection-level QoS support for multi-service mobile networks,” IEEE Trans. Wireless Commun., vol. 1, no. 3, pp. 521-530, July 2002. [19] S.-H. Oh and D.-W. Tcha, “Prioritized channel assignment in a cellular radio network,” IEEE Trans. Commun., vol. 40, no. 7, pp. 1259-1269, July 1992. [20] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, (1990). [21] R. Ramjee, R. Nagarajan, and D. Towsley, “On optimal call admission control in cellular networks,” in Proc. IEEE INFOCOM’96, pp. 29-41. [22] M. Schwartz, “Network management and control issues in multimedia wireless networks,” IEEE Personal Commun., vol. 2, no. 3, pp. 8-16, June 1995. [23] S. Tekinary and B. Jabbari, “A measurement based prioritization scheme for handovers in cellular and micro-cellular networks,” IEEE J. Select. Areas Commun., vol. 10, no. 7, pp. 1343-1350, Oct. 1992. [24] S. Wu, K. Y. M. Wong, and B. Li, “A dynamic call admission policy with precision QoS guarantee using stochastic control for mobile wireless networks,” IEEE/ACM Trans. Networking, vol. 10, no. 2, pp. 257-271, Apr. 2002. [25] C. H. Yoon and K. Un, “Performance of personal portable radio telephone systems with and without guarded channels,” IEEE J. Select. Areas Commun., vol. 11, no. 6, pp. 911-917, Aug. 1993. Tat-Chung Chau received the B.Sc. and M.Phil. degrees in Physics from the Hong Kong University of Science and Technology, in 1998 and 2001, respectively. He is now working in the area of systems support and development for the investment banking industry. His research interest is in wireless networks. Recently, he is active in promoting open source computer solutions to the general public.
K. Y. Michael Wong received the B.S. degree in Physics from the University of Hong Kong in 1978, and the M.S. and Ph.D. degrees in Physics from the University of California, Los Angeles, in 1982 and 1986, respectively. He worked as a Postdoctoral Research Associate with the Imperial College, London, U.K., and the University of Oxford, Oxford, U.K. In 1992, he became a Faculty Member with the Hong Kong University of Science and Technology, where he is now an Associate Professor in Physics. His research interests include stochastic processes and applications in telecommunications, learning theory, complex optimization, and multiagent systems. Bo Li (S’89-M’92-SM’99) received his B. Eng. (summa cum laude) and M. Eng. degrees in the Computer Science from Tsinghua University, Beijing in 1987 and 1989, respectively, and the Ph.D. degree in the Electrical and Computer Engineering from the University of Massachusetts at Amherst in 1993. Between 1993 and 1996, he worked on high performance routers and ATM switches in IBM Networking System Division, Research Triangle Park, North Carolina. Since 1996, he has been with the Department of Computer Science, Hong Kong University of Science and Technology. He has held an adjunct researcher position at the Microsoft Research Asia (MSRA), Beijing, China. His current research interests are on adaptive video multicast, packet scheduling, capacity planning in mobile wireless systems, scheduling and energy efficient routing in ad hoc networks, across layer design for sensor networks, and content distribution and replication. He has published approximately 80 journal papers and held several patents. He received the Outstanding Overseas Young Scientist Award from Natural Science Foundation of China in 2004. He has been on editorial board for 16 journals and involved in organizing more than 40 conferences, especially IEEE Infocom since 1996. He was the Co-TPC Chair for IEEE Infocom 2004.
