Call Admission Control for QoS Provisioning in ... - Semantic Scholar

IEICE TRANS. COMMUN., VOL.E82–B, NO.1 JANUARY 1999

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PAPER

Call Admission Control for QoS Provisioning in Multimedia Wireless ATM Networks Doo Seop EOM† , Masashi SUGANO†† , Masayuki MURATA† , and Hideo MIYAHARA† , Members

SUMMARY In this paper, we investigate a call admission control (CAC) problem in a multimedia wireless ATM network that supports various multimedia applications based on micro/pico cellular architectures. Due to reduced wireless cell size (compared to conventional cellular networks), forced termination of calls in progress becomes a more serious problem in the wireless ATM network. Another problem specific to the multimedia wireless network is how to avoid an excessive delay of non-realtime applications under the presence of various realtime applications with priority over non-realtime applications. We consider two service classes; CBR for realtime applications and UBR for nonrealtime applications, and then propose a new CAC scheme that addresses above two problems while minimizing a blocking probability of newly arriving calls of CBR. Through the analytical methods, we derive the blocking probabilities and forced termination probabilities of CBR calls and the average packet delay of UBR connections. We also present a method that decides the optimal CAC threshold values in our CAC scheme. key words: wireless ATM, CAC (call admission control), hand-

o, blocking probability, QoS (quality of service) 1.

Introduction

Wireless asynchronous transfer mode (wireless ATM) systems have been proposed for next-generation broadband and multimedia personal communication. The wireless ATM network is expected to provide a seamless connection between a mobile terminal and wired ATM networks so that multimedia applications supporting video, voice, and data can be implemented at the mobile terminal [1]. In order to support multimedia applications, several service classes have been standardized in the wired ATM world; those include CBR (Constant Bit Rate), VBR (Variable Bite Rate), UBR (Unspecified Bite Rate), and ABR (Available Bit Rate) service classes. However, the wireless ATM should be simple for ease of implementation. We therefore consider two service classes among them; CBR for realtime applications such as video and voice, and UBR for nonrealtime applications such as data. For an underlying multiple access scheme for the wireless ATM, we consider TDMA (Time Division Multiple Access) since only such a mechanism can guaranManuscript received June 22, 1998. Manuscript revised September 10, 1998. † The authors are with the Faculty of Engineering Science, Osaka University, Toyonaka-shi, 560-8531 Japan. †† The author is with the Osaka Prefectural College of Health Sciences, Habikino-shi, 583-8555 Japan.

tee the required bandwidth in the CBR service class. We assume that an appropriate combination of the cell level and bit level FECs (Forward Error Correction) effectively guarantees the cell loss probability as QoS (Quality of Service) parameter [2]. A remaining problem is then how GoS (Grade of Service) is assured in the wireless ATM environment, which is one of main subjects in this paper. Here, we use the terms QoS and GoS to denote cell level and call level quality of services, respectively. In the wireless ATM network, we need to consider two kinds of GoS in the CBR service class; a blocking probability of newly arriving calls and a forced termination probability that calls in progress are forced to be terminated due to handoff blocking. Since in the wireless ATM network environment, a radius of the wireless cell is typically in a range from 100m to 500m to achieve broadband transmission, handoff events due to user mobility tend to occur more frequently compared to conventional cellular networks [3]. Since forced termination of calls in progress is less desirable than blocking of new calls from a viewpoint of GoS guarantees to users, the forced termination probability must be at least less than the new call blocking probability [4]. One of the ways to keep the forced termination probability low is to restrict the number of slots that new CBR calls can use. It can be achieved by reserving some slots for CBR handoff calls as proposed in [5], [6]. However, those papers do not consider the multi-rate CBR connections in spite of the fact that one of most important features of ATM is to allow a flexible use of the bandwidth. In this paper, to handle multi-rate CBR connections, we further classify the CBR class into subclasses according to the bandwidth that the CBR connections require. We then consider the CAC problem by taking account of GoS (i.e., the new call blocking probability and the forced termination probability) of each CBR subclass. For the UBR service class, we assume that its connection attempt is always accepted irrespective of the number of slots used by the CBR connections. Thus, the main QoS parameter in the UBR service class becomes the packet delay. Here, by packet, we mean the protocol data unit of upper layer protocol than the ATM layer, i.e., the packet consists of several ATM cells. Generally, in the TDMA scheme, the CBR con-

EOM et al: CALL ADMISSION CONTROL FOR WIRELESS ATM

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nections are assigned slots periodically according to their bit-rate, and the UBR connections use the remaining slots. However, under such a simple bandwidth allocation scheme, the UBR connections may experience the quite large packet delay as the number of the CBR connections increases. It is especially undesirable for the interactive data applications such as remote logins and transaction processing. Therefore, CAC provisioning to assign the minimum number of slots to the UBR connections becomes important to avoid such an undesirable condition, which is another subject of this paper. While the CAC problem in cellular networks has been extensively studied in the past, most works have not considered multiple service classes. In [4] and [7], they considered voice and data as the realtime and nonrealtime applications, respectively, but their works are not enough to be applied to the wireless ATM networks where various realtime applications must be supported. In [8], they studied a CAC problem in the wireless ATM networks, but they did not consider the handoff problem, while it is very important in the wireless ATM as described before. In this paper, we propose a new CAC scheme suitable to the wireless ATM networks such that both of constraints on the forced termination probabilities of CBR subclasses and the packet delay of UBR are satisfied. Our CAC scheme restricts new calls of each CBR subclass by the CAC threshold (i.e., the number of slots that new calls of each CBR subclass can use). For this purpose, we present an efficient analytic method to derive the new call blocking and forced termination probabilities of CBR subclasses and the average packet delay of UBR connections under our CAC scheme. We also present an efficient search algorithm to decide the optimal CAC threshold values for CBR subclasses that minimize the new call blocking probabilities while satisfying both of the above constraints. This paper is organized as follows. In the next section, we explain the system model under consideration and our CAC scheme appropriate for the wireless ATM networks. We then present the analytic method to derive GoS metrics of each CBR subclass and the average packet delay of UBR in Sect. 3. Section 4 contains a description of the search algorithm to decide the optimal CAC threshold values. We discuss the performance of our CAC scheme through numerical examples in Sect. 5. Section 6 is devoted to concluding remarks. 2.

System Model Descriptions

2.1 CAC in TDMA Based Wireless ATM Network In the current study, a TDMA/TDD (Time Division Multiple Access/Time Division Duplex) type protocol in [9] is chosen as a multiple access method to implement an underlying physical structure. TDMA/TDD has been adopted by several wireless ATM prototype implementations [10], and we believe that the method

Fig. 1

Radio frame structure.

is best suitable to realize the mechanism of QoS guarantees among the existing protocols. As shown in Fig. 1, TDMA/TDD protocol can divide a fixed length frame into uplink (from terminal to base station) and downlink dynamically, so that it is applicable to the environment where the demand of both directions changes dependent on time. However we will assume that uplink and downlink slots are fixed in this paper for simplicity. The downlink part consists of preamble, control data (i.e., ACK) and data slots from the base station to terminals. In the uplink part, mini-slots for reservation are added to schedule the transmissions from terminals. In the protocol, when a new call of CBR service class arrives at the terminal, the terminal requests the number of slots required for that call, using slotted ALOHA protocol (see [9] for more details). If this connection request is accepted by CAC module, the required number of slots are then assigned to the terminal periodically by the base station. If not, the base station returns the negative acknowledgment for the call, and the terminal gives up a connection establishment attempt (i.e., call blocking). The number of slots reserved within each frame corresponds to the bandwidth guaranteed for the CBR service class connection. Such a periodic slot assignment continues until the call is terminated in the wireless cell or until the terminal carrying the call moves into another wireless cell. That is, in wireless ATM networks, the call duration is not always equal to the slot occupancy time in the wireless cell due to mobility of terminal (user). In Sect. 3, we will describe an effective analytic method that derives the new call blocking and forced termination probabilities of CBR calls by considering the effective slot occupancy time. For the delay-tolerant applications, we consider the UBR service class as described in Sect. 1. Slots for the UBR service class are assigned dynamically on a frame basis. The reservation is performed in a same manner to the CBR service class except that the unit of reservation is packet. Slot assignments for transmission of packets are scheduled by the base station according to FIFO or round robin policy. We note again that the slot request of UBR is always accepted irrespective of the number of slots used by the CBR connections. That is, the UBR service class is not an object of CAC. In


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other words, even if there is no available slot, UBR is accepted and then waiting for slots to be available unlike CBR blocked immediately. 2.2 CAC Policy From the viewpoint of users, forced termination of calls in progress is more serious GoS degradation than blocking of new calls. We therefore give priority to handoff calls over new calls so that the forced termination probability can be less than the new call blocking probability. That is, handoff calls are accepted without restriction if available slots exist, but new calls are accepted only when the total number of available slots are larger than the previously determined value (the CAC threshold which we will determine according to our CAC policy). Then, we introduce a strict constraint on the forced termination probability at the expense of increase in the new call blocking probability. As a result, the wireless link becomes less utilized because the amount of handoff traffic also decreases as blocking of new calls increases. However, it does not always mean a disadvantage in the multimedia environment. We have the UBR traffic, and the average number of slots that the UBR connections can use becomes large, i.e., the reduced packet delay of UBR connections can be attained. Therefore, by the CAC thresholds, we can assure both the forced termination probabilities of CBR and the packet delay of UBR. In what follows, we describe our CAC scheme in more detail. Let the number of data slots per frame be L and the number of slots required for CBR subclass i (i = 1, 2, · · · , K) be bi . Here, we use the term CBR subclass to classify multi-rate CBR connections. The CAC threshold for CBR subclass i is denoted as Ni . See below for its definition. In each wireless cell, CAC is performed for the new calls initiated in that cell and the handoff calls from other cells as follows. • The case that a new call of CBR subclass i arrives. If the sum of the number of the currently occupied slots and the slot requirement for the newly arriving call (bi ) is less than or equal to Ni , the new call is accepted. If not, it is blocked. In other words, by letting mi be the number of the currently accepted connections of CBR subclass i, the new call is accepted only if the following condition is met. Ni ≥

K X

mj bj + bi

L≥

K X

mj bj + bi

Our CAC scheme tries to minimize the new call blocking probabilities of CBR subclasses while satisfying the constraints on the forced termination probabilities of CBR subclasses and the packet delay of UBR. Therefore, it is necessary to decide the optimal CAC threshold values for the given traffic intensity and constraints of both service classes, which will be discussed in Sect. 4 after we develop an analytic tool to handle our problem in Sect. 3. 3.

Analysis

3.1 New Call Blocking and Forced Termination Probabilities of CBR Class We first describe traffic models of calls and wireless cells with user mobility. We assume that the call arrivals of CBR subclass i in a wireless cell follow a Poisson distribution with rate λi , and that the call durations are exponentially distributed with mean 1/µi . Furthermore, the time that calls stay in the wireless cell before moving into other wireless cells also follows an exponentially distribution with mean 1/hi . Therefore, each call moves into other wireless cell with probability pi = hi /(µi + hi ) or terminates in the current wireless cell with probability 1 − pi = µi /(µi + hi ). Then, the mean duration that the call spends in one wireless cell equals 1/(µi + hi ). The average number of handoff events before the call normally terminates (without handoff blocking) is given as pi /(1 − pi ) = hi /µi . Furthermore, let PBi be the blocking probability of new calls and PHi be the probability that handoff calls are dropped due to lack of available slots when moving into other wireless cells. The traffic model for the call of CBR subclass i is depicted in Fig. 2. We further assume that the flow between a designated wireless cell and its adjacent wireless cells is conservative. That is, the rate with which calls in the designated wireless cell move out to its adjacent wireless cells is equal to the rate with which calls in its adjacent wireless cells enter the designated wireless cell. The

(1)

j=1

• The case that a handoff call of CBR subclass i moves into a designated wireless cell from other wireless cells. If the number of idle slots is more than or equal to bi , the handoff call is accepted. If not, on the other hand, it is dropped. The condition for accepting the handoff call is expressed as follows.

(2)

j=1

Fig. 2

Traffic model for a call.


17 1 π(m1 , m2 ) = π(m1 + 1, m2 )(m1 + 1) µλ11+h +g1 2 X for 0 ≤ b1 + mj bj ≤ N1

j=1 1 π(m1 , m2 ) = π(m1 + 1, m2 )(m1 + 1) µ1g+h 1 2 X for N1 ≤ b1 + mj bj ≤ L

j=1

Fig. 3

2 π(m1 , m2 ) = π(m1 , m2 + 1)(m2 + 1) µλ22+h +g2 2 X for 0 ≤ b2 + mj bj ≤ N2

Flow model for a wireless cell.

j=1 2 π(m1 , m2 ) = π(m1 , m2 + 1)(m2 + 1) µ2g+h 2 2 X for N2 ≤ b2 + mj bj ≤ L

j=1

                    

(4)

                    

(5)

Since all π(m1 , m2 ) can be expressed in terms of π(0, 0) by solving the above local balance equations recursively, they can be easily obtained from the normalization condition given by; b bL c b 1 X

m1 =0

Fig. 4 Markov chain model for obtaining slot occupancy distribution.

flow model of the designated wireless cell, say cell A, is depicted in Fig. 3, where the flow rate is denoted as gi . Then, the probability PTi that calls in progress are terminated due to handoff events, which we refer to as the forced termination probability, can be given by; PTi =

∞ X j=0

pj+1 (1 − PHi )j PHi = i

h i P Hi µi + hi PHi

(3)

Next, we consider a Markov chain for our model where the state represents the numbers of calls of CBR subclasses in the wireless cell. As an example, in Fig. 4, we show the case where the number of CBR subclasses is two (K = 2), the number of data slots per frame L = 6, and the CAC thresholds N1 = N2 = 4, and the numbers of slot requirement b1 = 1 and b2 = 2. Let π(m1 , m2 ) be the steady state probability that there are m1 of CBR subclass 1 calls and m2 of CBR subclass 2 calls in the cell. Then, the local balance equations of the Markov chain can be given as follows;

L−m1 b1 b2

X

c

π(m1 , m2 ) = 1

(6)

m2 =0

where bxc denotes the largest integer value less than or equal to x. The approach can be easily extended for a more general case, i.e., K > 2, to obtain the steady state probability π(m) where m represents a 1 × K vector whose i-th element is mi . Let q(j) be the steady state probability that the number of occupied slots is j. Furthermore, let us introduce b for a K × 1 vector whose i-th element is bi . Then q(j) can be obtained as follows; X π(m) (7) q(j) = all m such that mb = j The blocking probability of newly arriving calls in CBR subclass i is given by; PBi =

L X

q(j)

(8)

j=Ni −bi +1

Similarly, the probability PHi that handoff calls of CBR subclass i are dropped due to lack of available slots is given by; P Hi =

L X

q(j)

(9)

j=L−bi +1

Since gi also depends on PBi and PHi , we need an iterative method. More specifically, as having been shown in Fig. 3, the rate of the flow into a wireless cell includes the rates of the accepted new arrivals and handoff traffic, which is given by; λi (1 − PBi ) + gi (1 − PHi )

(10)

Since the accepted calls leave the wireless cell with


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probability pi , the flow rate gi with which calls move toward adjacent wireless cells can be determined as follows; pi {λi (1 − PBi ) + gi (1 − PHi )}

(11)

In summary, we determine PBi and PHi according to the following procedure. 1. Set PBi = PHi = 0 and gi = λi pi /(1 − pi ) = λi hi /µi as the initial conditions. 2. Solve local balance equations for obtaining π(m). See Eqs. (4) through (6) for K = 2. 3. Determine PBi and PHi using Eqs. (7) through (9). 4. Set gi = pi {λi (1 − PBi ) + gi (1 − PHi )}. 5. Repeat steps 2 through 4 until convergence is reached. After obtaining PBi and PHi , we finally determine the forced termination probability for each CBR subclass using Eq. (3). 3.2 Average Delay of UBR Class Packets In the previous subsection, we have evaluated the GoS metrics of each CBR subclass without considering the UBR traffic since we assume that the UBR traffic is given lower priority and therefore it does not affect the performance of CBR class calls. On the contrary, the packet delay of UBR can not be determined without considering the CBR traffic since the UBR packets reserved by the base station use the leftover slots after the CBR connections are assigned slots. We assume that the packet arrivals of UBR in the wireless cell are Poisson with rate λ, and the packet lengths are exponentially distributed with mean l. Furthermore, the UBR packets are scheduled according to a FIFO (First-In-First-Out) service discipline by the base station. The average packet delay consists of the delay for slot reservation, the waiting time for available slots, and the packet transmission time. However, due to space limitation, we only focus on the effect of CBR traffic upon the packet delay of UBR in the below although additional delays such as the delay for slot reservation should also be considered for the completeness of UBR class packet delays. An analytic method to derive the slot reservation delay can be found in [9]. Unlike the CBR connection immediately transmitted at constant rate corresponding to its slot requirement by the base station after accepted by CAC, the transmission of the reserved UBR packets is delayed until slots to be available and its transmission rate depends on the number of slots used by the CBR connections. Therefore, the transmission process of the UBR packets on the wireless link can be modeled by a queuing system with varying service rate as shown in Fig. 5. We note that the bandwidth used by the CBR service class can be viewed as near constant in analyzing the UBR service class since the duration of CBR

Fig. 5

Transmission process of UBR packets.

connection is much longer than the packet transmission time of UBR connections. Thus, we can use an M/M/1 queue in determining the UBR packet delay by assuming that its system capacity is virtually set to the available bandwidth to the UBR service class. Let E [D|j] denote the average packet delay of UBR under the condition that j slots out of total C (< L) slots are occupied by the CBR connections. Here, we introduce another threshold C since if all of slots are occupied by the CBR service class calls, the UBR packets never be transmitted, which leads to infinite delays. The average packet delay of UBR packets is determined by using the analysis results for the M/M/1 queue. We then obtain the average packet delay E [D] by considering the distribution of slot occupancy by the CBR service class as follows; E [D] =

C X

E [D|j] q(j)

(12)

j=0

where q(j) was given by Eq. (7). 4.

Determination of Optimal CAC Thresholds

In this section, we determine the optimal CAC threshold values to minimize the new call blocking probabilities of CBR subclasses while satisfying both of the constraints on the forced termination probabilities of CBR subclasses and the average packet delay of the UBR class. In doing so, we assume that the offered traffic of each service class is estimated a priori. As having been shown in the previous section, the new call blocking probability PBi of CBR subclass i decreases as the CAC threshold Ni increases. On the other hand, the forced termination probability PTi of CBR subclass i increases as the CAC threshold Ni increases. That is, PBi (PTi ) is a monotonically decreasing (increasing) function of Ni . Also, the average packet delay of UBR E [D] is a monotonically increas-


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ing function of Ni because the number of CBR connections increases as Ni increases. From the above observation, if we have only a single CAC threshold, the optimal value is a maximum of the CAC threshold values satisfying both of the constraints on PTi and E [D]. That is, when the number of CBR subclasses K is one, we can find the optimal CAC threshold value by using a well known binary search algorithm. However, it is not so simple to find the optimal CAC threshold values for the case of multiple CAC thresholds. We therefore propose the following procedure. Recall that m = (m1 , m2 , · · · , mK ) denotes a 1×K vector whose i-th element mi represents the number of calls in progress of CBR subclass i, for i = 1, · · · , K. Let N = (N1 , N2 , · · · , NK ) denote a 1×K vector whose i-th element Ni represents the CAC threshold of CBR subclass i. Then, it is evident that our CAC policy is coordinate convex since calls of CBR subclass i can be more accepted as Ni increases. In other words, for given N , if (m1 , · · · , mi , · · · , mK ) is an admissible state and mi is greater than zero, then (m1 , · · · , mi − 1, · · · , mK ) is also an admissible state. By using this property, we can reduce the number of cases which must be tested in finding the optimal CAC threshold values. For simplicity, we will explain our algorithm for the case of K = 2, but the algorithm can easily be extended to a general case. In the case of K = 2, the number of possible cases for the optimal N is equal to L × L. However, the coordinate convex property of our policy can reduce the number of searches. For example, once N2 is determined as 8 for N1 = L, we can start search from N2 = 9 for the case N1 = L − 1 because the values in a range from (L − 1, 0) to (L − 1, 8) are not optimal due to the coordinate convex property. We summarize our algorithm; 1. Find the optimal value of N2 for the case N1 = L by using the binary search algorithm. It is used as the initial value of N2 . 2. Decrease the value of N1 by one. 3. Iterate the following steps, 3.1 through 3.4. 3.1 Set N2 = N2 + 1. 3.2 Calculate PBi , PTi and E [D]. 3.3 If not satisfying the constraints, set N2 = N2 − 1 and go to Step 4. 3.4 If PBi is less than the current optimal value, save the values of N1 , N2 and PBi as the current optimal values. 4. Repeat Steps 2 and 3 until the value of N2 reaches L or the value of N1 reaches one. 5. If the optimal value is not found, the algorithm fails. By utilizing the coordinate convex property of our policy and the monotonicity of PBi , PTi and E [D], our

search algorithm can easily be extended for the case where K is greater than two and different threshold values can be determined for CBR subclasses. No CAC thresholds satisfying the given constraints under the given traffic intensity may not be found. It indicates that the constraints are too strict for given capacity and traffic intensity. It should be solved by appropriate network provisioning, but it can not be avoided by unpredictable overload traffic. In this paper, we do not deal with the problem on how to set again the constraints by considering the fairness among service classes under an overload condition of wireless cell. It is left to be a future research topic. We have determined the optimal CAC threshold values assuming that the traffic intensity of each service class is given. To cope with dynamically varying traffic intensity, however we need to monitor traffic streams and then update the optimal CAC threshold values based on the estimated traffic intensity of each service class. The problem then becomes whether the above algorithm can be performed within the time. In what follows, we briefly explain one promising method to update the optimal CAC threshold values as the traffic intensity of each service class varies with time. In [11], the authors observed that traffic volume changes considerably with time-of-day and there is a traffic pattern during a typical weekday, according to traffic measurement over nine months. It suggests that call arrival rate depends considerably on time-of-day but there is little variation in the call arrival rates which are measured in the specific periods (e.g., 1 p.m.–2 p.m.) of typical weekdays. From the above observation, it must be reasonable to calculate the CAC threshold values for the specific period of the day by using only the traffic statistics for the corresponding period. Also, there is very little call arrivals in the late night period (12 a.m.–7 a.m.) so that updating of CAC thresholds is not necessary during that period. It is because the largest value that CAC thresholds can have is always determined as the optimal value of each CAC threshold when there is very little call arrivals. The base station thus have enough time to calculate the CAC threshold values for the next day during that period. By doing this, the base station can spend enough time to calculate the optimal CAC threshold values when the updating period of CAC thresholds is not too short. We next consider the complexity of our algorithm. Unfortunately, we found difficulty in determining the complexity of our algorithm mainly because the number of iterations needed to end the loop in our algorithm depends on the traffic condition. Instead, we evaluated the execution time of our algorithm. We compared the execution time of our algorithm with that of the algorithm in [12] which finds the optimal CAC threshold values using the binary search algorithm. Table 1 shows the result of comparison on Sun 4/80 (SPARC station 10) when the number of CBR subclasses K is two and


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5 slots are always reserved for UBR (i.e., L − C = 5). The numbers of slots required for two CBR subclasses (CBR1 and CBR2) are chosen as b1 = 1 and b2 = 4. For the traffic parameters of CBR subclasses, the values shown in Table 3 of Sect. 5 is used. The constraint on the forced termination probability is chosen as 0.005 for both CBR subclasses. For the UBR service class, we assume that the packet arrivals are Poisson with rate λ = 4.95 [packets/sec], and the packet lengths are exponentially distributed with mean of 8 Kbytes. The constraint on the average packet delay is chosen as 60 msec. In this case, our algorithm is 5.19–14.92 times faster than the binary search based algorithm over the range of L considered. The difference between the execution times of two algorithms depends only on the number of CAC thresholds combination tested in each algorithm. In the case of the binary search based algorithm, when K = i, it performs binary search Li−1 times for obtaining the optimal CAC threshold values. Therefore, the number of CAC thresholds combination tested is equal to Li−1 × (1 + log L). On the other hand, in the case of our algorithm, the number of CAC thresholds combination is not always proportional to K and L. As shown in Table 1, the execution time of our algorithm for L = 130 can be smaller than even that for L = 110. It is because when L = 130, the traffic load becomes small compared to the link capacity so that the initial value of N2 is determined as the value close to L. Then, N2 reaches L before N1 becomes one. That is, in this case, the number of CAC thresholds combination to be tested becomes small although L becomes large. When L is less than 130, our algorithm is not terminated until N1 becomes one. This is the worst case for our algorithm. Considering the worst case, the number of CAC thresholds combination can be approximately determined as Li−1 + (1 + log L) because in most cases, our algorithm leaves the loop in Step 3 at first iteration. For the reason above, as the traffic load is small compared to the link capacity or the less strict constraints are used, the difference between the execution times of two algorithms becomes large. Also, the difference becomes much larger than that of the worst case as the number of CBR subclasses increases. It is because in the case of the binary search based algorithm, Table 1 L 50 60 70 80 90 100 110 120 130

Comparison of execution times.

Our algorithm (sec) 7.83 14.69 25.24 39.92 58.58 92.57 145.46 230.22 125.53

Binary Search (sec) 40.67 78.19 155.30 217.69 366.54 586.69 930.24 1332.93 1873.09

the number of CAC thresholds combination to be tested does not depend on the traffic load and the constraints; on the other hand, in the case of our algorithm it becomes much smaller than that of the worst case as the traffic load is small compared to the link capacity or the less strict constraints are used. Even if the traffic load variation does not make a change in the number of CAC thresholds combination to be tested, it can give an effect upon the execution time of our algorithm. It is because the iteration for obtaining PBi and PHi is the most time consuming part and the time taken until the values of PBi and PHi are converged is likely to be changed with the amount of traffic load. Of course, the above discussion is also applied to the binary search based algorithm because the iteration is common to both algorithms. Therefore the relative difference between the execution times of two algorithms still holds. 5.

Numerical Examples and Discussions

In this section, we present numerical examples in our CAC scheme. We consider two types of CBR traffic, requiring different number of slots as shown in Table 2. We assume that the uplink and downlink parts of the frame have a same length, and 10% of the link capacity is used for control data and reservation mini-slots. Each CBR stream is divided into ATM cells using AAL/1 (47 byte payload) format. In the following examples, we assume that 5 slots are always reserved for UBR, i.e., L − C = 5. In what follows, we first fix the CAC threshold values for CBR subclasses as given values (N1 = N2 ). It is necessary to show how those parameters and other system parameters affect the system performance (forced termination probabilities, new call blocking probabilities and UBR packet delays). The proposed algorithm presented in the previous section is then applied to demonstrate how our algorithm works. First, we show how the new call and forced termination probabilities of each CBR subclass vary under the given traffic load when changing the CAC threshold. For the traffic parameters of CBR subclasses, we have used the values shown in Table 3. Namely, the average number of handoff events before normal termination of each call becomes five, i.e., hi /µi = 5. As shown in Fig. 6, if we restrict the number of newly arriving calls by reducing the CAC threshold, the forced termination probability of each CBR subclass becomes Table 2

Parameters for the underlying TDMA.

Channel speed Frame length Total number of slots (L) CBR1 data rate Number of slots for CBR1 (b1 ) CBR2 data rate Number of slots for CBR2 (b2 )

25 5.71 129 64 1 256 4

Mbps msec Kbps slot/frame Kbps slots/frame


21 Table 3

Traffic parameters for CBR subclasses 1 and 2.

Call arrival rate of CBR1, λ1 Call arrival rate of CBR2, λ2 Call duration of CBR1, 1/µ1 Call duration of CBR2, 1/µ2 Time CBR1 spends in a cell, 1/h1 Time CBR2 spends in a cell, 1/h2

0.03 0.03 500 500 100 100

calls/sec calls/sec sec sec sec sec

Fig. 7 Effect of the average number of handoff events upon the new call blocking probability.

Fig. 6 Variation of the new call blocking and forced termination probabilities when changing the CAC threshold.

smaller than the value for the case where no CAC threshold is provided (i.e., N1 = N2 = 124). On the other hand, the new call blocking probability of each CBR subclass becomes larger. Therefore, it is necessary to decide the values of CAC thresholds by considering both the new call blocking probabilities and the forced termination probabilities, which indicates the importance of the appropriate CAC threshold values; just our objective in the current paper. We also investigate how the average number of handoff events before normal termination of calls gives an effect upon our CAC scheme. We have compared the new call blocking and forced termination probabilities for the three cases; 1/h1 = 1/h2 = 50, 100, 1000. The values shown in Table 3 are used for λi and µi . That is, the case of 1/hi = 50 corresponds to that the average number of handoff events before normal termination of calls is 10. The new call blocking and forced termination probabilities for CBR subclass 1 are shown in Figs. 7 and 8, respectively. Note that due to space limitation, we do not present results for CBR subclass 2, but we observed the same tendency in CBR subclass 2. In Fig. 7, we observe that the difference between the new call blocking probabilities is negligible. It means that the average number of handoff events gives little effect upon the new call blocking probability. On the other hand, in Fig. 8, we observe that the difference between the forced termination probabilities is considerably large. Also, in the case of 1/hi = 1000 (the smallest average number of handoff events), the forced termination probability decreases most rapidly as the CAC threshold becomes small. From the above observations, we can see that when handoff events do not

Fig. 8 Effect of the average number of handoff events upon the forced termination probability.

occur frequently, we can reduce the forced termination probability with less increase in the new call blocking probability. That is, the effect of our CAC scheme increases as the average number of handoff events decreases. Therefore, the handoff rate hi becomes an important factor in determining the CAC threshold values. Next, we show how the average packet delay of UBR varies under the given traffic load when changing the CAC threshold. We assume that the packet arrivals of UBR in a wireless cell are Poisson with rate λ [packets/sec], and the packet lengths are exponentially distributed with mean of 8 Kbytes. The arrival rates of new calls of CBR subclasses are chosen as λ1 = 0.25 and λ2 = 0.01. For the other traffic parameters of CBR subclasses, we have used the values shown in Table 3. In Fig. 9, we observe that the average packet delay of UBR becomes small as the CAC threshold decreases. It is because the amount of CBR traffic including the handoff traffic becomes small as the CAC threshold decreases. That is, the average number of slots available to UBR increases as the CAC threshold decreases. Therefore, we can bound the average packet delay of UBR under the certain level if the values of CAC thresholds are appropriately chosen. Of course, we also need to consider


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Fig. 9 Variation of the average packet delay of UBR when changing the CAC threshold.

Fig. 10 Variation of the optimal CAC threshold value when changing the CBR and UBR traffic loads.

the forced termination probabilities of CBR subclasses for that purpose. We can confirm that the maximum CAC threshold value satisfying both of the constraints on PTi and E [D] is optimal. It is due to the monotonicity nature of functions PBi , PTi and E [D] (see Fig. 6 and Fig. 9) as described in Sect. 4. Finally, we investigate how the traffic load and constraints give an effect upon our CAC scheme in following examples. For simplicity, we assume that the number of CBR subclasses is one, i.e., only CBR1 is considered. We use 0.01 and 0.001 for the constraint on the forced termination probability as in [7], [13]. Corresponding handoff dropping probabilities can be calculated by using Eq. (3). Figure 10 shows how the optimal CAC threshold value varies when changing the CBR and UBR traffic loads. The constraints on the forced termination probability and the average packet delay are chosen as 0.01 and 60 msec, respectively. As one can expect, we can see that the UBR traffic load gives little effect upon the optimal CAC threshold value at lower load region of the CBR traffic since enough slots for satisfying the constraint on the average packet delay are available to the UBR traffic in this case. However, at higher load region of the CBR traffic, the optimal CAC threshold

Fig. 11 Variation of the optimal CAC threshold value when less strict constraints are used.

value becomes small to increase the average number of slots available to the UBR traffic so that the constraint on the average packet delay can be satisfied as the load of UBR traffic increases. Figure 11 shows how the optimal CAC threshold values are changed when more strict constraint is used. The constraint on the forced termination probability is decreased to 0.001. We can observe that the optimal CAC threshold values become slightly smaller than those of Fig. 10 but are not so changed over the range of the load of UBR traffic we have examined. The observation is also applicable even at higher load region of the CBR traffic. This result comes from the fact that for satisfying more strict constraint on the forced termination probability, it is necessary to reduce the number of slots allowed for new CBR calls. It can be achieved by decreasing the CAC threshold until enough slots to guarantee the forced termination probability are available for CBR handoff calls. Namely, the wireless link becomes less utilized by CBR traffic compared to Fig. 10 because the amount of handoff traffic also decreases as a result of an increase in the new call blocking probability. Therefore, the constraint on the average packet delay can be satisfied without decreasing CAC threshold value when the load of UBR traffic increases even at higher load region of the CBR traffic. 6.

Conclusion

We have studied the call admission control problem in the wireless ATM network based on micro/pico cellular architectures that supports various multimedia applications. The proposed CAC scheme can bound the forced termination probability of CBR calls in progress and the average packet delay of UBR while minimizing the blocking probability of newly arriving CBR calls by selecting the appropriate CAC threshold values. Also, an efficient search method is proposed to find the optimal threshold value for each CBR subclass. Through the numerical examples, we have shown that the constraints on the forced termination probability of CBR


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and the average packet delay of UBR can be satisfied at the expense of increase in the new call blocking probability. It can be achieved by restricting the number of slots that new CBR calls can use. References [1] C.K. Toh, “WIRELESS ATM and AD-HOC NETWORKS —Protocols and Architectures,” Kluwer Academic Publishers, 1997. [2] M. Sugano, D. S. Eom, M. Murata, and H. Miyahara, “A combination scheme of ARQ and FEC for error correction of wireless ATM networks,” Proc. ITC-CSCC ’97, pp.517– 520, 1997. [3] D. Raychaudhuri, “Wireless ATM networks: Architecture, system, design and prototyping,” IEEE Personal Communications, vol.3, no.4, pp.42–49, Aug. 1996. [4] F. Callegati, C. Carciofi, M. Frullone, P. Grazioso, and G. Riva, “Call admission control for multi-service packet switched cellular mobile radio systems,” IEICE Trans. Commun., vol.E78-B, no.4, pp.504–512, April 1995. [5] M. Naghshineh and M. Schwartz, “Distributed call admission control in mobile/wireless networks,” IEEE J. Sel. Areas Commun., vol.14, no.4, pp.711–717, May 1996. [6] C.H. Yoon and C.K. Un, “Performance of personal portable radio telephone systems with and without guard channels,” IEEE J. Sel. Areas Commun., vol.11, no.6, pp.911–917, Aug. 1993. [7] M. Naghshineh and A.S. Acampora, “QoS provisioning in micro-cellular networks supporting multiple classes of traffic,” Wireless Networks, vol.2, pp.195–203, 1996. [8] S.K. Biswas and B. Sengupta, “Call admissibility for multirate traffic in wireless ATM networks,” Proc. IEEE INFOCOM ’97, pp.650–658, 1997. [9] D.S. Eom, M. Sugano, M. Murata, and H. Miyahara, “A combination scheme of ARQ and FEC for multimedia wireless ATM networks,” IEICE Trans. Commun., vol.E81-B, no.5, pp.1016–1024, May 1998. [10] J. Mikkonen, C. Corrado, and C. Evci, “Emerging wireless broadband networks,” IEEE Commun. Mag., vol.36, no.2, pp.112–117, Feb. 1998. [11] D. Lam, D.C. Cox, and J. Widom, “Teletraffic modeling for personal communications services,” IEEE Commun. Mag., vol.35, no.2, pp.79–87, Feb. 1997. [12] R. Ramjee, R. Nagarajan, and D. Towsley, “On optimal call admission control in cellular networks,” Wireless Networks, vol.3, no.1, pp.29–41, 1997. [13] C. Chao, W. Chen, and C. Jackson, “Connection admission control for mobile multiple-class personal communications networks,” Proc. ICC ’97, pp.391–395, 1997.

Doo Seop Eom received the B.E. and M.E. degrees in Electronics Engineering from Korea University, Seoul, Korea, in 1987 and 1989, respectively. He joined the Communication Systems Division, Electronics and Telecommunications Research Institute (ETRI), Korea, in 1989. Since 1996, he has been studying at Osaka University, Japan, first as a research student and now as a Ph.D. candidate, with a Japanese Government Scholarship. His research interests include communication network design and wireless ATM.

Masashi Sugano received the B.E., M.E., and Dr.E. degrees in Information and Computer Sciences from Osaka University, Osaka, Japan, in 1986, 1988, and 1993, respectively. In 1988, he joined Mita Industrial Co., Ltd., Osaka, as a Researcher. Since September 1996, he has been an Associate Professor of Osaka Prefectural College of Health Sciences. His research interests include design and performance evaluation of computer communication networks, network reliability, and wireless network systems. He received the IEICE paper award in 1991. Dr. Sugano is a member of the IEEE.

Masayuki Murata received the B.E., M.E., and Dr.E. degrees in Information and Computer Sciences from Osaka University, Osaka, Japan, in 1982, 1984, and 1988, respectively. In April 1984, he joined Tokyo Research Laboratory, IBM Japan, as a Researcher. From September 1987 to January 1989, he was an Assistant Professor with Computation Center, Osaka University. On February 1989, he moved to the Department of Information and Computer Sciences, Faculty of Engineering, Osaka University, and he has been an Associate Professor since December 1992. His research interests include computer communication networks, performance modeling and evaluation, and queuing systems. Dr. Murata is a member of the IEEE and ACM.

Hideo Miyahara received the M.E. and D.E. degrees from Osaka University, Osaka, Japan in 1969 and 1973, respectively. From 1973 to 1980, he was an Assistant Professor in the Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto, Japan. From 1980 to 1986, he was an Associate Professor in the Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Osaka, Japan. From 1986 to 1989, he was a Professor of the Computation Center, Osaka University. Since 1989, he has been a Professor in the Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University. From 1995, he is a director of Computation Center of Osaka University. From 1983 to 1984, he was a Visiting Scientist at IBM Thomas J. Watson Research Center. His research interests include performance evaluation of computer communication networks, broadband ISDN, and multimedia systems. Prof. Miyahara is a fellow of the IEEE.