Wireless Netw (2008) 14:121–131 DOI 10.1007/s11276-007-0042-9
Fixed and dynamic bandwidth allocation strategies for wireless mobile integrated services networks Nagla O. Mohamed Æ Dervis Z. Deniz
Published online: 10 July 2007 Springer Science+Business Media, LLC 2007
Abstract Performance evaluation of two bandwidth allocation strategies in wireless mobile integrated services networks is carried out. Performances of the proposed strategies are compared with those of the traditional guard channels and threshold strategies. In the study, a single wireless cell which is accessed by voice and non-voice traffic types producing, respectively narrowband and wideband calls is considered. In the proposed strategies a number of channels are reserved in a fixed or dynamic fashion for the use of originating wideband calls in addition to the guard channels allocated for the handoff calls. The results indicate that the two strategies have comparable advantages and by manipulating the number of reserved channels, desired performance levels can be achieved. The dynamic reservation based strategy makes the system fairer for the originating wideband calls while maintaining low handoff dropping probability and acceptable channel utilization levels. On the other hand, the fixed reservation strategy provides a lower handoff call dropping at comparable channel utilization levels. The tradeoff is between improving the handoff call dropping versus the originating wideband call blocking. Both strategies provide better performance for the originating wideband calls compared
Dervis Z. Deniz—Senior Member of the Institute of Electrical and Electronics Engineers (SMIEEE). N. O. Mohamed Electrical and Electronics Engineering Department, University of Khartoum, Khartoum, Sudan D. Z. Deniz (&) Information Technologies R&D Center, Eastern Mediterranean Department of Electrical & Electronics Engineering, Eastern Mediterranean University, Gazimagusa, Mersin-10, Turkey e-mail:
[email protected]
with that provided by the traditional guard channels strategy. Keywords Call admission control Handoff Bandwidth reservation Wireless mobile Guard channels
1 Introduction Future wireless networks are expected to support a wide range of traffic types such as audio, video, data and speech. These traffic types have different bandwidth and quality of service (QoS) requirements. Supporting all these traffic types in one network, leads to a number of challenges. The widely differing characteristics of these traffic types e.g., data traffic consumes more bandwidth than voice and the limited wireless resources have to be utilized effectively and allocated fairly to the different traffic types. In addition to that, in wireless networks, a mobile user which has been handed from another cell should not have the connection lost due to mobility i.e., handoff call dropping should be as low as possible. Thus, Call Admission Control (CAC) strategies in wireless networks are required to guarantee that each of the different traffic types achieves its QoS and bandwidth requirements and at the same time to decrease the probability of handoff call dropping as much as possible. One of the most popular strategies for wireless mobile multimedia networks which serve different types of customers with differing bandwidth requirements is the Reserve Channels (RC) or Guard Channels (GC) CAC strategy. In this strategy, the available transmission channels are divided into two groups: active channels (A) which can be used by all traffic types (originating and handoff) and guard channels (G) which are reserved for the exclusive use of handoff customers, as an ‘‘overflow’’
123
122
group of channels. This guarantees low blocking probability for handoff customers. The guard channels CAC strategy however, is unfair to customer types which have higher bandwidth requirements since the active channels are completely shared among all customer types. Thus, customers with lower bandwidth requirements fill up any free channels while a higher bandwidth customer can not be accepted for service until all its required bandwidth is available. This problem is compounded if the arrival rate of the lower bandwidth requiring customers is high. The Guard Channels CAC for voice traffic has been dealt with extensively in the literature [1–3]. The number of studies which deal with CAC for systems which serve two or more traffic types is limited. CAC for systems which serve two types of customers with both customers requiring only one channel for their service is studied in Trivedi et al. [4]. Studies Lee et al. [5] and Kwon et al. [6] deal with the Threshold CAC strategy (TS) in systems which serve more than one customer type and each customer type requires a different number of channels for its service. Li et al. [7] studies the performance of complete sharing and dynamic partitioning CAC strategies in an integrated voice/ data cellular system. The complete sharing and complete partitioning CAC strategies for narrowband and wideband traffic are considered in Pavlidou [8]. In Epstien and Schwartz [9], the guard channels CAC strategy for a system which serves both voice and data traffic is studied but with the introduction of a queue for handoff data traffic. In Deniz and Mohamed [10], a comparison of the performance of the guard channels and threshold CAC strategies in wireless cells which serve narrowband and wideband traffic is presented. Wang et al. [11] is a study of a complete partitioning strategy for real time and non-real time traffic. The channels are divided into three regions; one for each type of traffic and a third region for the overflow of handoff calls of both types. In this paper, we investigate two new variations of the traditional guard channels CAC strategy in order to overcome its shortcomings for wideband traffic. In the first, originating n-type calls are prevented from using a fixed number of channels from the active channels, while originating wideband calls and handoff calls can access all the active channels. In the second strategy, a dynamic boundary is formed whereby an originating narrowband call which on arrival finds a certain number of free channels is blocked from service. Mathematical models for these two strategies are developed. Performances of the two strategies are compared with those of the well known guard channels and threshold CAC strategies. The rest of this paper is organized as follows; a description of the proposed fixed and dynamic reservation strategies is given in Sect. 2. Section 3 presents the analytical models of the two strategies. Numerical results
123
Wireless Netw (2008) 14:121–131
and discussions of these results are given in Sect. 4. Section 5 presents the conclusions.
2 Proposed call admission control strategies Two call admission control strategies, namely the Guard Channels CAC with Fixed Reservation (GCFR) and the Guard Channels CAC with Dynamic Reservation (GCDR) strategies are proposed. The schematic representation of these CAC strategies are depicted in Fig. 1(a) and (b). It is assumed that each wireless cell has a total of m channels or basic bandwidth units (BBUs) and two types of customer arrivals; n-type and w-type. N-type customers require bandwidth, bn = 1 BBU for their service and could correspond to the voice applications. W-type customers need bandwidth, bw ‡ 1 BBUs for their service and could represent data or video type applications. The bw channels are assumed to be seized and released simultaneously. These strategies are descried in detail below. 2.1 Guard channels CAC with fixed reservation (GCFR) The schematic representation of this CAC strategy is depicted in Fig. 1(a). The channels are divided into two groups; active channels, A and guard channels, G. Active channels are further divided into two groups; shared, S and restricted, R channels. The group S is completely shared by all types of calls; originating and handoff. The group R is a reserved (or restricted) group of channels and admittance of originating calls is based on certain access rules. In this work, the aim is to make the system fairer to the originating w-type calls; thus, originating n-type calls are prevented from using the R channel group. The G group of channels can only be used by handoff calls of both types; this increases the success rate of handoff requests. 2.2 Guard channels CAC with dynamic reservation (GCDR) The schematic representation of this CAC strategy is depicted in Fig. 1(b). The channels are divided into active channels, A and guard channels, G. Active channels are further ‘‘soft’’ divided into two groups; the shared, S and a restricted access virtual group R which is allowed to have a variable number of channels and a special rule for its channel allocation. The G group of channels can only be used by handoff calls of both types. As in the static reservation case, the aim of this strategy is to make the system fairer to originating w-type calls, while maintaining good access probability for the handoff calls. The algorithm for handling of originating calls is
Wireless Netw (2008) 14:121–131
(a)
BBUs
Originating n-type calls Originating w-type calls
Shared Group
S
Handoff n-type calls
Total number of BBUs in a cell , m
Fig. 1 Guard channels CAC with (a) fixed reservation (b) dynamic reservation
123
A
R Handoff w-type calls
G
(b)
BBUs
Originating n-type calls Originating w-type calls Handoff n-type calls
Total number of BBUs in a cell, m
Shared Group S A R ≤ (b w-x) +1
Handoff w-type calls
bw x
G
Fig. 2 The flow chart for the procedure for handling originating calls
New call arrival
Yes
x≤
fA(K)
≤ bw
Yes n-type ?
?
No
fA (Κ) ≥ b w ?
No
Yes
No
fA (K) ≥ b n ?
Yes
call accepted
No
call blocked
shown in Fig. 2. The basic idea is to reject originating ntype calls as long as there is the possibility of accepting one more originating w-type call. When the number of free
active channels, fA(K), (where K is a vector composed of Kn, Kw, the number of n-type and w-type customers in the system, respectively), becomes less than bw + 1 but greater
123
124
than or equal to x, where x is an integer number between 1 and bw, originating n-type calls will be blocked. Thus, as long as x fA ðKÞ bw ; originating n-type calls will be rejected. That is the reserved group, R is not permanent, it exists only when the condition x fA ðKÞ bw is satisfied. The number of reserved channels, R is also variable. During the period when the condition x fA ðKÞ bw is satisfied, R can be anything from R = x to R = bw. Effectively, for the values of 0 fA ðKÞ\x the restricted access group R does not exist, while for x fA ðKÞ bw ; the value of R is dynamically variable in the range given by x £ R £ bw. The value of x can be chosen to have a value say equal to bw/2. Once the number of free channels becomes greater than bw, blocking of originating n-type calls is stopped. Originating w-type calls are always served as long as there are enough free active channels for their service. The overall motivation in this technique is to provide a feature similar to the ‘‘hold-back n channels’’ scheme such that if the number of free channels is above a certain threshold limit, then accumulation of free channels can be speeded up by not allowing their use by the originating n-type calls. This increases the chance of an originating w-type call to find at least bw free channels available at its arrival epoch. The value of x should not be too low since it will increase call rejections for originating n-type calls. Similarly, there is not much point in making the x value too high either, since that will not cause significant reduction in the blocking probability of the w-type calls.
3 Performance evaluation The arrivals for n-type and w-type customers are assumed to be Poisson distributed with mean rates kn and kw calls per time unit, respectively. Call holding times of n-type and w-type customers are assumed to be exponentially dis1 tributed with means l1 n and lw time units, respectively. Handoff call arrivals for the two types of customers also form Poisson processes with mean rates an and aw calls per time unit, respectively. The cell residence time (CRT) i.e., the amount of time during which the two types of mobile users stay in a cell, is assumed to follow an exponential distribution with means h1 and h1 n w time units for the narrowband and wideband traffic types, respectively. Therefore, the channel holding time, HTn (or HTw) of a call is equal to the smaller of the values lx and hx, where x : = n | w. The memoryless property of the exponential pdf leads to E{HTx} = 1/(lx + hx). 3.1 The GCFR CAC strategy This CAC strategy can be modeled as a two-dimensional Markov chain. The state space is given by Eq. 1 where Kw
123
Wireless Netw (2008) 14:121–131
and Kn are the number of w-type and n-type customers in the system at any time. E :¼
K : Kn ¼ 0; 1; . . . ; m; Kw ¼ 0; 1; . . . ; d; d ¼
m bw
ð1Þ
The number of w-type and n-type customers being served in state K, Sw(K) and Sn(K) can be calculated using the following equation: Sw ðKÞ ¼ Sw ðKÞ ¼
Kw and Sn ðKÞ ¼ Kn if ðKn bn þ Kw bw Þ m 0 and Sn ðKÞ ¼ 0 otherwise: ð2Þ
The number of free shared channels S in state K, fS(K), the number of free reserved channels R in state K, fR(K), and the number of free guard channels, fG(K) are given by: fS ðKÞ ¼ S u; fR ðKÞ ¼ R and fG ðKÞ ¼ G if u S fS ðKÞ ¼ 0; fR ðKÞ ¼ A u and fG ðKÞ ¼ G; if S\u A fS ðKÞ ¼ 0; fR ðKÞ ¼ 0 and fG ðKÞ ¼ m u; otherwise; ð3Þ where u = Sn(K)bn + Sw(K)bw, and represents the total number of channels in use. The number of free channels available to n-type, w-type and handoff customers of both types, fn(K), fw(K) and fH(K), respectively are calculated using Eq. 4, fn ðKÞ ¼ fS ðKÞ fw ðKÞ ¼ fS ðKÞ þ fR ðKÞ fH ðKÞ ¼ fS ðKÞ þ fR ðKÞ þ fG ðKÞ:
ð4Þ
The two-dimensional Markov chain representation of the system states is shown in Fig. 3 where dw = [A/bw] and dn = A–R = S. From Fig. 3, the following global balance equations can be formed: fkn Iðfn ðKÞbn Þþan IðfH ðKÞbn Þþkw Iðfw ðKÞbw Þ þaw IðfH ðKÞbw Þ þSn ðKÞðln þhn ÞþSw ðKÞðlw þhw ÞgpðKÞ þfkn Iðfn ðKÞbn Þþan IðfH ðKÞbn ÞgIðKn >0ÞpðKe2 Þ þfkw Iðfw ðKÞbw Þþaw IðfH ðKÞbw ÞgIðKw >0ÞpðKe1 Þ þSn ðKþe2 Þfln þhn gpðKþe2 Þ þSw ðKþe1 Þflw þhw gpðKþe1 Þ¼0; K2E; ð5Þ where e1 ¼ ð1; 0Þ; e2 ¼ ð0; 1Þ and I(x) is the indicator function of event x and its value is 1 if event x is true and 0 otherwise. p(K) is the steady state probability of the system being in state K. From probability theory, the sum of state probabilities over all the state space of the system should be equal to 1.
Wireless Netw (2008) 14:121–131
125
Fig. 3 The Markov chain representation of the guard channels CAC with fixed reservation
d, 0
d(µw+θw)
d w+1, 1
(d w+1)(µw+θw)
.
.
1, 2
(µn +θn)
(λw+αw)
. . .
(λw+αw)
(λn +αn )
(λw+αw)
(λn +αn ) 0, 2
(µw+θw)
. . .
(λw+αw)
1, d n+1
(µw+θw)
αn 0, d n
2(µn +θn)
(µn+θn )
. (d n+1)(µn+θn )
(µw+θw)
0, 1
αn
1, d n
2(µn +θn)
(µw+θw)
0, 0
.
(λn +αn ) 1,1
.
.
. . . (λn +αn )
.
.
.
d w,1
(µn +θn )
1, 0
(µw+θw)
.
αw
(λn+αn) d w,0
.
.
αw
.
.
(dw+1). (µw+θw)
(µn +θn )
.
(λn+αn)
d w+1, 0
. . .
number of w- type cus tomer s in the s ystem, Kw
.
.
. . .
.
αw
(d n+1)(µn +θn )
. . .
(λw+αw)
αn 0, d n+1
. . .
0, m
m(µn +θn )
number of n-type customers in the system, Kn
This is called the normalizing condition and is given by the following equation: X pðKÞ ¼ 1 ð6Þ
kw Iðfw ðKÞ bw Þ þ aw IðfH ðKÞ bw Þ;
K2E
To solve for the state probabilities, p(K), the global balance equations and the normalizing equation can be written in matrix format as follows: Qp ep
where all blocks are square matrices of order m + 1. The structure of the sub-matrices is shown below. The matrix A0 is diagonal with elements equal to
¼ 0 ¼ 1
ð7Þ
where p is a column vector made up of the state probabilities, p(K) and e is the row vector whose elements are all equal to 1. Q is the transition matrix, whose elements are derived from the global balance equations. The structure of the Q matrix is as shown in Eq. 8. 2
A0;1 6 A0;2 6 6 6 6 Q¼6 6 6 6 6 4
A1;0 A1;1 A1;2
3 A2;0 A2;1 A2;2
A3;0 A3;1
A4;0 Ad1;0 Ad1;1 A0
7 7 7 7 7 7; 7 7 7 7 A2 5 A1
ð9Þ
where K = (Kw, Kn) are the states: {Kw = d–1, Kn = 0, 1,…, m}. The matrices Av2 ; 0 v d 2; are all diagonal matrices with all diagonals given by Eq. 9 and where K = (Kw, Kn) are the states: {Kw = v, Kn = 0, 1,…, m}. The matrix A2 is a diagonal matrix with diagonal entries given by Sw ðKÞflw þ hw g;
ð10Þ
where K = (Kw, Kn) are the states: {Kw = d–1, Kn = 0, 1,…, m}. Matrices Av0 ; for 1 £ v £ d – 1, are diagonal matrices with diagonal entries given by Eq. 10 and where K = (Kw, Kn) are the states: {Kw = v, Kn = 0, 1,…, m}. The matrix A1 is a Jacobi matrix of order m + 1. The elements on its inferior diagonal are given by kn Iðfn ðKÞ bn Þ þ an IðfH ðKÞ bn Þ:
ð11Þ
The elements on the superior diagonal are given by ð8Þ
Sn ðK þ e2 Þfln þ hn g:
ð12Þ
123
126
Wireless Netw (2008) 14:121–131
The diagonal elements are given by ½kn Iðfn ðKÞ bn Þ þ an IðfH ðKÞ bn Þ þkw Iðfw ðKÞ bw Þ þ aw IðfH ðKÞ bw Þ þSn ðKÞfln þ hn gþSw ðKÞflw þ hw g;
BPw ¼ ð13Þ
i¼0
ð14Þ
0; fR ðKÞ ¼ A u A u; fR ðKÞ ¼ 0 fS ðKÞ ¼ 0; fR ðKÞ ¼ 0;
if x A u bw ; and otherwise and
where R, the rate matrix is the minimal non-negative solution of Eq. 15 A1 R þ A0 ¼ 0
ð15Þ
Finally, the vector xd ; is calculated using xd ¼ Rxd1
ð16Þ
The blocking probabilities of the two traffic types (BPn, BPw) and the probability of handoff call dropping for the two customer types (PHDn, PHDw) can be calculated using Eqs. 17–20. The mean server utilization, E(U) can be calculated using Eq. 21.
BPn ¼
X K2E
123
pðKÞIðfn ðKÞ\bn Þ
ð18Þ
PHDn ¼
X
pðKÞIðfH ðKÞ\bn Þ
ð19Þ
pðKÞIðfH ðKÞ\bw Þ
ð20Þ
fSn ðKÞbn þ Sw ðKÞbw gpðKÞ:
ð21Þ
K2E
A0;1 x0 þ A1;0 x1 ¼ 0 Ai1;2 xi1 þ Ai;1 x0 þ Aiþ1;0 xiþ1 ¼ 0; 1 i d 2; Ad2;2 xd2 þ Ad1;1 þ RA2 xd1 ¼ 0; d2 P exi þ eðI þ RÞxd1 ¼ 1
pðKÞIðfw ðKÞ\bw Þ
K2E
where in Eqs. 11–13, K = (Kw, Kn) are the states: {Kw = d, Kn = 0, 1,…, m}. The matrices Av1 ; 0 v d 1; are Jacobi matrices of order m + 1. The elements on their inferior diagonal are given by Eq. 11, the elements on the superior diagonal are given by Eq. 12 and the diagonal elements are given by Eq. 13 where in this case, K = (Kw, Kn) are the states: {Kw = v, Kn = 0, 1,…, m}. The column vector, p can be written as T p ¼ xT0 xT1 xTd where xi are column vectors of size m + 1. The xi vectors can be obtained by solving the following set of linear equations:
fS ðKÞ ¼
X
ð17Þ
PHDw ¼
X K2E
EðUÞ ¼
X K2E
3.2 The GCDR CAC strategy This CAC strategy can also be modeled as a two-dimensional Markov chain. The state space is given by Eq. 1. The number of w-type and n-type customers being served in state K, Sw(K) and Sn(K) can be calculated using Eq. 2. The number of free shared channels in state K, fA(K), the number of restricted channels which w-type as well as handoff customers can use, fR(K) and the number of free guard channels, fG(K) are given by:
fG ðKÞ ¼ G if u A
ð22Þ
fG ðKÞ ¼ m u otherwise
where u = Sn(K)bn + Sw(K)bw. The number of free channels available to n-type, w-type and handoff customers of both types, fn(K), fw(K) and fH(K), respectively are calculated using Eq. 4. The system states can be represented by the twodimensional Markov chain of Fig. 3. The global balance equations of the system are given by Eq. 5. The blocking probabilities of the two traffic types and the probability of handoff call dropping for the two customer types can be calculated using Eqs. 17–20 while the mean server utilization can be calculated by Eq. 21.
4 Numerical results and discussions In this section, numerical results are presented. A comparison between the two proposed CAC strategies, guard channels (GC) and threshold (TS) CAC strategies is made.
Wireless Netw (2008) 14:121–131
A sample system configuration with m = 48 BBUs, A = 32 BBUs, G = 16 BBUs, bw = 6 BBUs and bn = 1 BBU is selected for evaluating the system behavior. l–w 1 = 200 s, l–1 n = 100 s, kw = 1/30 call arrivals/s, kn varies from 1/20 to 10/20 call arrivals/s, an = 1/2 kn, aw = 1/2 –1 kw call arrivals/s and h–1 n = hw = 100 s. An event driven simulation system was also developed to validate the accuracy of the calculations. To alleviate the transient effect, the simulation was run for a long duration in order to reach the steady state, and the system performance measures were obtained using 20 independent replications. Figures 4–8 show that the simulation results agree very well with the analytical results. So as to be able to fairly compare the performance of the two strategies, we need to select parameters which give the same operating conditions for both strategies. For the dynamic reservation strategy, x is assumed to be bw/2; that is an originating n-type call which on its arrival finds bw/2 £ fA(K) £ bw free active channels is lost. Therefore, the number of channels in the virtual partition cannot exceed (bw–(bw/2)) + 1 (in this case (6–3) + 1 = 4 BBUs). Thus, for our comparison, for the fixed reservation strategy (GCFR), we choose R = 4 BBUs. Figures 4–8 show the comparison of the TS, GC, guard channels with fixed reservation (GCFR) and guard channels with dynamic reservation (GCDR), CAC strategies. For the threshold CAC strategy, we set tn = 14, (the threshold for originating ntype calls) and tw = 3 i.e, at any time 14 originating n-type calls and three originating w-type calls will be accepted into the system. These values are selected to correspond to the case of setting aside G = 16 channels for handoff calls. From Fig. 4, considering the GC, GCFR and GCDR strategies, it is observed that the blocking probability of originating n-type calls is lowest for the GC strategy
127
Fig. 5 Blocking probability of originating w-type calls versus qn (qw = 2.2)
Fig. 6 Probability of n-type handoff call dropping versus qn (qw = 2.2)
Fig. 4 Blocking probability of originating n-type calls versus qn (qw = 2.2)
followed by the GCFR strategy (beyond approx. qn = 12 value). This is expected because the GC strategy is not fair to calls with high bandwidth requirements. This leads to a lower blocking probability for lower bandwidth requiring calls (n-type in this case). The fixed reservation strategy results in increased blocking of n-type calls, while with the dynamic reservation strategy, BPn reaches its highest curve (except for the TS which beyond approx. qn = 13.8 value has the highest BPn curve). That is, the dynamic reservation strategy reduces the priority of the originating n-type calls the most. One exception to the above is the behavior of the threshold strategy. Its performance curve rises steeply beyond the qn = 5 value and passes the GCDR curve values beyond approx. qn = 13.8 value. This is also expected since the threshold strategy has a maximum
123
128
Fig. 7 Probability of w-type handoff call dropping versus qn (qw = 2.2)
Fig. 8 Percentage mean server utilization, E(U) versus qn (qw = 2.2)
threshold value defined for the number of n-type calls in the system. Hence, it becomes inflexible for arrival rates above a given value and results in increase in the blocking probability of n-type calls. From Fig. 5, the blocking probability of originating w-type calls BPw, is highest for the GC strategy which is also expected due to the unfairness of this strategy to calls of higher bandwidth requirements. This is followed by the GCFR strategy. The dynamic reservation strategy (GCDR) performs the best; giving the least BPw (for approx. qn£ 12 value). For qn > 12 it still provides the least BPw value compared to the GC and GCFR strategies. This is due to the increased blocking of originating n-type calls which leaves more space for originating w-type calls to be accepted to the system. The threshold strategy gives a con-
123
Wireless Netw (2008) 14:121–131
stant blocking probability since the value of the qw is set at 2.2 for this particular experiment. The w-type calls are not in competition for the channels with n-type calls since the maximum number of n-type calls in the system can not exceed the value of threshold for n-type calls, tn. Figures 6 and 7 show the probability of handoff call dropping for the n-type and the w-type calls versus the traffic intensity for the originating n-type calls, respectively. From these figures, it is clear that the GCFR strategy performs the best of the four strategies giving the least handoff call dropping for both traffic types (for qn > 5 values). That is, if originating n-type calls are prevented from accessing a number of active channels, handoff call dropping is actually reduced. The probability of blocking of n-type handoff calls is the highest for the GCDR strategy when compared to strategies which use channel reservation. The Threshold CAC gives almost constant BPw over all values of qn (see Fig. 5). From this, we can say that the Threshold CAC makes the system more fair to w-type calls. But looking at Figures 6 and 7, the Threshold CAC strategy gives the highest handoff call dropping for both types of calls which defeats the main aim of wireless CAC strategies (i.e., as low handoff call dropping as possible). The percentage mean server utilization is shown in Fig. 8. Among the strategies, that use channel reservation, the traditional GC strategy achieves the highest server utilization when using this configuration. This is expected because in both fixed and dynamic reservation strategies, we are preventing calls from being served while there are idle channels. Dynamic reservation has slightly higher mean server utilization than the fixed reservation strategy. The threshold CAC strategy has the highest overall utilization between the region of 7 < qn < 17. All in all, even though, the threshold CAC performs very well in terms of utilization, it gives very high values for probability of handoff call dropping for both call types. The main aim of this work is to make the guard channels CAC strategy fairer to originating w-type calls. Fairness can be considered from two aspects; from the users’ point of view and from the service provider’s point of view. Users want to have more equitable response from the system. In the traditional guard channels strategy, from the point of view of w-type customers, the system is rather ‘‘un-fair’’. Thus, a fair strategy would even out the differences between the w-type and n-type customers in terms of their blocking probabilities. In this work, ‘‘fairer’’ is considered to mean a reduction in BPw. It can be said that this aim has been partially achieved in the sample configuration given above. Greater improvement of the system performance in terms of ‘‘fairness’’ to originating w-type calls can be achieved if the number of R channels is increased. Figures 9–13 show the performance of the fixed and dynamic reservation strategies when the number of R
Wireless Netw (2008) 14:121–131
Fig. 9 Blocking probability of originating calls versus the number of channels in the R region when using fixed reservation strategy (qn = 2.5, qw = 2.2)
Fig. 10 Blocking probability of originating calls versus the maximum number of channels in the virtual partition, R when using dynamic reservation strategy (qn = 2.5, qw = 2.2)
channels is varied. Note that for the dynamic reservation strategy the R value can be increased only until it becomes equal to bw BBUs. In these figures, kn = 1/20 calls/s and kw = 1/30 calls/s are selected while the rest of the parameters remain the same. Figures 9 and 10 show BPi (i = n,w) when R is increased in increments of 1 BBU for fixed and dynamic reservation. From Fig. 9, it is observed that at R = 1, BPn is much lower than BPw. When the number of reserved active channels R, starts to increase, BPw decreases while BPn increases. At the point where R = bw–bn number of BBUs, the two blocking probabilities become equal (i.e., BPn = BPw). After this point, BPw has a lower value than BPn. This phenomenon is observed to be independent of
129
Fig. 11 Probability of handoff call dropping versus the number of channels in the R region when using fixed reservation (qn = 2.5, qw = 2.2)
Fig. 12 Probability of handoff call dropping versus the maximum number of channels in the virtual partition, R when using dynamic reservation (qn = 2.5, qw = 2.2)
the traffic intensity. It is also worth noting here, that as R increases, the increase in BPn is much more pronounced than the decrease in BPw which suggests that the value of R should be a small value so that the effect on BPn will not be too drastic. Figure 10 shows that the value of BPw also starts off higher than the value of BPn. The point of intersection of the two curves is at the point of R = 2.75. Thus, for this strategy, there is no practical point at which BPn = BPw (because we cannot set R as a fraction). It is also interesting to note that the difference in blocking probabilities, |BP2–BP1| = 0.008 is approximately the same at R = 2.5 and at R = 3.0. Another interesting point to note
123
130
about this figure is that the value of BPw is almost constant at all values of R. Figure 11 shows the values of PHDi, for 1 < R < 32 for the case of GCFR strategy. It is observed that for the PHDw, the curve has multiple saddle points and multiple humps. The saddle points occur at values of R = 3, 8, 15, 22 and 28. The humps occur at multiples of bw (i.e., at R = 6, 12, 18, 24 and 30). The minimum value of PHDw occurs at R = 3. PHDw is higher than PHDn at all values of R. This is due to the higher bandwidth requirements of w-type calls. Further, PHDn curve is almost constant at all values of R. This is because n-type handoff calls can find accommodation within the A + G group of channels much more easily than the w-type handoff calls. Figure 12, shows that for dynamic reservation (GCDR) strategy, the highest handoff call dropping for the w-type customers, PHDw occurs at R = 3 and it begins to decrease slightly after that point reaching its minimum point at R = 6. It is interesting to note that for the same range of R values (namely R = 1–6), the values of PHDw have similar handoff call dropping probabilities. This is true for the PHDn as well. However, in the same range of 1£ R£ 6 values, for the GCFR strategy, the minimum and maximum points occur at the values of R = 3 and 6 BBUs, respectively, while for the dynamic reservation strategy, the same R values represent the maximum and minimum values for PHDw, respectively. Figure 13 shows that the dynamic reservation strategy has higher mean server utilization for E(U) in the region 1£ R < bw for the given traffic intensities. The server utilization has its peak value when R = 1 and then it starts to decrease. This is expected because as the number of R channels increases, more channels are sitting idle while n-type calls are being blocked from service. Therefore, depending on the value of R, whatever type of performance required for originating calls can be
Fig. 13 E(U) versus the number R channels (qn = 2.5, qw = 2.2)
123
Wireless Netw (2008) 14:121–131
achieved; that is, if BPw is to be less than BPn, a higher value of R should be chosen (i.e., more active channels will be reserved for the originating w-type calls). If on the other hand we require BPw and BPn to be equal (the system is fair in a sense), then the value of R = (bw–bn) would be chosen. The effect of reserving a number of active channels for originating w-type calls on handoff call dropping is rather small; while having a crucial effect in reducing the BPw significantly. When using fixed reservation, handoff call dropping is reduced (see Figs. 7 and 8). The point R = (bw–bn) is a significant point for the blocking probability of originating and handoff calls for the two strategies. The dynamic reservation (GCDR) strategy gives better performance (i.e., lower BPw) for the originating w-type calls than the fixed reservation strategy (GCFR) strategy. At the same time, fixed reservation strategy achieves the required goal of making the system fairer to originating w-type calls while decreasing the probability of handoff call dropping. In wireless networks, the primary objective is reducing the handoff call dropping as much as possible. Although from the above, the performance of dynamic reservation is as good as the performance of fixed reservation, it suffers from a major drawback; namely, in the current chosen settings, the number of R channels can not be greater than bw. However, this may be modified within the model. A matrix algorithmic solution technique was developed to obtain the state probabilities of the system. The solution technique is general and it can be used to solve most CAC strategies for this type of system. It makes use of the special structure of the Markov chain to break the transition matrix into sub-matrices, which means less memory and storage requirements leading to a much faster solution time.
5 Conclusions In this paper, two new variations of the guard channels CAC strategy for wireless multimedia networks namely, guard channels with fixed reservation (GCFR) and guard channels with dynamic reservation (GCDR) are presented. The performance of the two strategies are then studied and compared with a number of well known strategies including the traditional guard channels (GC) and the threshold (TS) CAC strategies. From the results obtained, we can conclude that: (1) reserving either a fixed or changing number of active channels for originating w-type (higher bandwidth requiring) calls results in a system which is fairer to the originating w-type calls; (2) the effect of this reservation on handoff call dropping is very small; (3) changing the number of reserved active channels can result in whatever type of performance required; (4) fixed reservation results in a reduction in handoff call dropping; (5) the dynamic reservation technique provides by far the greatest changes
Wireless Netw (2008) 14:121–131
in the blocking probabilities of the originating calls; increases it for the n-type calls and reduces it to comparable levels for the w-type calls for the given traffic loads. In this work, only the case of two customer classes is considered. They map broadly to integration of narrowband and wideband requiring traffic classes such as voice and video traffic. It is entirely feasible to extend this technique to include more traffic types; in that case, there would need to be more than one reserve channels regions for the originating customers. For example, a three customer class system will need two reserved channels regions. The probability of w-type handoff call dropping, PHDw has a rather high value when compared with the probability of n-type handoff call dropping. This is due to their high bandwidth requirements. Making the system fairer to the w-type handoff calls is an area of further research.
References 1. Hong, D., & Rappaport, S. S. (1986). Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and non-prioritized handoff procedures. IEEE Transactions on Vehicular Technology, VT-35(3), 77–92. 2. Guerin, R. (1988). Queuing blocking system with two arrival streams and guard channels. IEEE Transactions on Communications, 36(2), 153–163. 3. Soh, W.-S., & Kim, H. S. (2001). Dynamic guard bandwidth scheme for wireless broadband networks. Proceedings of IEEE INFOCOM 2001, 1, 572–581. 4. Trivedi, K. S., Selvamuthu, D., & Ma, X. (2002). Analytic modeling of handoffs in wireless cellular networks. In Proceedings of 6th Joint Conference on Information Sciences (pp. 1383– 1392) March 2002, Raleigh, NC. 5. Lee, J. Y., Bahk, S., & Kim, S. (2000). Cell-oriented admission control for QoS support in wireless multimedia networks. IEE Electronics Letters, 36(21), 1826–1828 6. Kwon, T., Kim, S., Choi, Y., & Naghshineh, M. (2000). Threshold-type admission control in wireless/mobile multimedia networks using prioritized adaptive framework. IEE Electronics Letters, 36(9), 852–853. 7. Li, B., Li, L., Li, B., & Cao, X.-R. (2003). On handoff performance for an integrated voice/data cellular system. Wireless Networks, 9(4), 393–402. 8. Pavlidou, F.-N. (1994). Mixed media traffic cellular systems. IEEE Transactions on Communications, 42(2/3/4), 848–853. 9. Epstien, B., & Schwartz, M. (1995). Reservation strategies for multimedia traffic in a wireless environment. In Proceedings of IEEE Vehicular Technology Conference (VTC’95) (pp. 165–169). 10. Deniz, D. Z., & Mohamed, N. O. (2003). Performance of CAC strategies for multimedia traffic in wireless networks. IEEE Journal for Selected Areas in Communications, 21(10), 1557– 1565. 11. Wang, J., Zeng, Q.-A., & Agrawal, D. P. (2003). Performance Analysis of a preemptive and priority reservation handoff scheme for integrated service-based wireless mobile networks. IEEE Transactions on Mobile Computing, 2(1), 65–75.
131
Author Biographies Nagla O. Mohamed obtained the B.S. and M.S. degrees in electrical and electronic engineering from University of Khartoum, in 1993 and 1998, respectively. She received the Ph.D. degree in electrical and electronic engineering, with computer network specialization from the Eastern Mediterranean University in Gazimagusa, N. Cyprus in July 2004. She joined the University of Khartoum, Department of Electrical and Electronic Engineering, Khartoum, Sudan, in September 2004 as a lecturer after returning from her research leave. She is currently following an academic career in the above department. Her research interests include computer networks, performance analysis, call admission control in wire-line and wireless networks. Dervis Z. Deniz received B.Sc.(Eng.) degree in electrical and electronic engineering and M.Sc. degree in electronics engineering from QMC and KCL, University of London in 1976 and 1977, respectively. He joined University College London, Department of Computer Science (UCL-CS) for research as a Commonwealth Scholar and obtained the Ph.D. degree from University of London in 1991 in the field of computer networks. He followed a career in professional engineering and worked as an R&D Electronics Engineer at GEC Telecommunications Ltd., Coventry (UK) and at Crosfield Electronics in London (UK), during 1978–1980. He then joined the Department of Electrical and Electronic Engineering, Eastern Mediterranean University (EMU) in Gazimagusa, Northern Cyprus in 1981 as a lecturer. He joined the same department after returning from research leave in 1991. He is a full professor, chairman of the department and the founding director of the Information Technologies R&D Center. He is an advisor to the Telecommunications Authority in Turkey. He is the author of many scholarly publications including a book entitled ISDN and Its Application to LAN Interconnection (London, McGraw-Hill, 1994). He is the holder of Science & Technology Award from the Istanbul Technical University (1995). His research interests include fast network technologies, network interconnection, dynamic bandwidth management, call admission control, multimedia traffic characterization, distance learning, software engineering, academic decision support systems, and engineering education. Dr. Deniz is a senior member of the IEEE Communications and Computer Societies, a member of IET (UK), ACM and SCS.
123
