1
QoS Provisioning with Distributed Call Admission Control in Wireless Networks Xusheng Tian and Chuanyi Ji Department of Electrical, Computer and System Engineering Rensselaer Polytechnic Institute, Troy, NY 12180 e-mail:
[email protected],
[email protected] Abstract— In this work, we investigate the performance of distributed admission control with QoS provisioning and dynamical channel allocation for mobile/wireless networks. We first provide a QoS metric feasible for admission control with dynamically allocated channels. We then derive analytically a criterion using the QoS measure for distributed call admission control with dynamic channel allocation. Since Maximum packing is used as the dynamic channel allocation scheme, the results obtained are independent of any particular algorithm which implements the dynamic channel assignment. Our results thereby provides the optimal performance achievable for the distributed admission control with the QoS provisioning by the best dynamic channel allocation scheme in the given setting.
I. Introduction One of the challenges to enabling multi-media services in wireless networks is how to support the guarantees of Quality of Service (QoS) with the limited capacity. Call admission control is needed to meet this challenge. As many admission control algorithms have been developed together with dynamic channel allocation, little has been done on the analysis to include QoS provisioning. The goal of this work is to investigate the fundamental questions: What is the achievable utilization under a given QoS constraint by distributed admission control with dynamically assigned channels? How much gain can dynamic channel allocation provide compared to the fixed channel allocation? In cellular systems, a geographical region is splitted into cells, each containing one base station. When a new call request is made at a cell, the decision can be made on either accepting or rejecting the call at each base station, and a channel can be assigned to the call admitted. This results in distributed admission control strategy which can be applied to every cell (base station). Such a strategy is suitable for large wireless systems with a changing topology. The admission control we consider in this work falls into this category. Two factors determine an admission decision: (1) the availability of a channel at a cell, and (2) the QoS constraints. Channels are made available at each cell by channel assignment schemes based on co-channel reuse constraints[1]. Under such constraints, two classes of channel assignment algorithms have been widely investigated: fixed channel assignment (FCA) and dynamic channel assignment (DCA)[2]. In a FCA scheme, a set of nominal channels are permanently assigned to each cell. An arriving call can only be accepted if To appear in ICC’98
there is a nominal channel available in that cell. Due to the short term temporal and spatial variations of the traffic in cellular systems, FCA schemes are not able to attain a high channel efficiency. To overcome this, DCA schemes have been studied. Unlike FCA, in DCA, all channels are kept in a central pool to be shared by all calls in every cell. A channel is eligible for use in any cell provided the co-channel reuse constraint is satisfied. [1] [3] [2] give a comprehensive overview on major existing algorithms for channel allocation. Although lots of channel allocation schemes have been investigated in the literature, most of them did not take QoS into consideration. The QoS in cellular networks is mainly determined by the new call blocking probability (PB ) and hand-off call dropping probability (PD ). The former is the fraction of new calls that are blocked, while the latter is the fraction of admitted calls that terminate prematurely due to lack of channels when trying to hand-off. Dropping a hand-off call is highly undesirable from users’ point of view. Therefore, the network should treat new call and hand-off call requests in a different manner and give hand-off calls a higher priority so that the chance of dropping a hand-off call is low. Those channel allocation schemes which do include the QoS provisioning are fixed channel allocation (denoted as FCAQoS). They include the guard channel policy [4] and distributed admission control with FCA-QoS [5]. In particular, [5] enforces a QoS constraint on the hand-off dropping probability to cellular networks with homogeneous traffic. As both [5] and [4] suggest the need to investigate the performance of DCA under QoS constraints, how to analyze the performance of DCA with QoS provisioning is still an open problem. Moreover, [5] and [4] consider FCA-QoS under spatially uniform traffic. Non-uniform traffic patterns have not been taken into consideration. The focus of this work is on analyzing the performance of distributed admission control with the QoS provisioning and dynamic channel allocation under both uniform and nonuniform traffic conditions. Two potential challenges are involved for this investigation. One is how to define a QoS metric in the framework of admission control with DCA. Another is how to formulate the problem in a general fashion, since the performance varies with respect to different algorithms which implement the dynamic channel assignments. How to define a QoS metric in the paradigm of DCA is still an open problem and a current active research area[5]. A commonly-used QoS measure is the hand-off dropping probability. Such a measure has been used in [5] for fixed channel
allocation as a threshold on the highest tolerable hand-off dropping probability. Since the hand-off dropping probability is hard to be evaluated directly, the threshold is used on the overload probability instead. As will soon become clear, this measure is not able to provide the QoS provisioning for the case of DCA, where the contribution of new calls to the overload probability is too significant to be neglected. Although a weighted sum of the blocking probability and the hand-off dropping probability may be used to circumvent this problem [6], a weighting factor needs to be determined, which can be somewhat arbitrary. We take a different approach to derive a QoS measure for the case of DCA through analyzing the contributions of the blocking and the hand-off dropping probabilities to the overload probability. The QoS measure thus obtained is a non-linear function of the thresholds on the blocking and hand-off dropping probabilities. Using our QoS measure, we will show that a QoS threshold on the handoff dropping probability alone will not be optimal as soon as the blocking probability is not negligible. We will also show experimentally that the QoS measure we obtain leads to an almost guaranteed QoS on the hand-off dropping probability under both uniform and non-uniform traffic conditions. To provide a general formation on the problem, we focus on providing the optimal performance for admission control with the QoS provisioning achievable by the best dynamic channel allocation scheme rather than investigating a specific DCA algorithm. This is accomplished by using maximum packing [7] [8] [9] as the dynamical channel allocation scheme. The results obtained are thus independent of any particular algorithm which implements the dynamic channel assignment. Motivated by FCA-QoS[5], we extend the analysis on distributed call admission control with FCA-QoS to DCA-QoS. We will derive analytically an admission control policy with DCA under the QoS constraint. We will show that the derived admission control policy leads to an 17% −30% increase in utilization compared to FCA-QoS under various traffic conditions. The results thereby provide the maximum possible increase in utilization by any DCA scheme compared to the FCA scheme in the same setting. This paper is organized as follows. In Section II, we describe our model. In Section III, we describe distributed admission control policies. In Section IV, we derive the implementing details of our policy. In Section V, we give numerical results, and compare the performance of our DCA-QoS with the FCA-QoS. we conclude the paper in Section VI. II. The Model Call Terminates
C i-2
n i-2
Ci-1
Ci
n i-1
ni
C i+1
n i+1
Ci+2
n i+2
handoffs
Call Arrivals
Fig. 1. 1-D cell array
We consider one-dimensional cellular systems with dynamic
2
channel allocation (DCA) schemes. Referring to Fig. 1, we denote Ci as cell i, and ni as the number of users in cell i. Ci−1 and Ci+1 are the left and right neighbors of Ci . Ci−2 is the left neighbor of Ci−1 , and Ci+2 is the right neighbor of Ci+1 . In addition, let ni−2 (t), ni−1 (t), ni+1 (t), and ni+2 (t) be the number of users in Ci−2 , Ci−1 , Ci+1 , and Ci+2 at time t, respectively. We assume that Ci is where a call admission request is being made. New call arrivals are assumed to be Poisson distributed with the arrival rate λi in Ci . Call lasting time is assumed to be exponentially distributed with the mean 1/µ. Inter-handoff time is also assumed to be exponentially distributed with the mean 1/h. Furthermore, new call arrivals, call hand-ups and call hand-offs are assumed to be mutually independent both within a cell and among cells. There are M distinct channels in the system. The channel reuse distance is assumed to be 2, i.e., a channel can be reused in every other cells. Two adjacent cells can support up to M calls simultaneously. Maximum packing (MP) is considered to be our DCA scheme. Our choice on MP strategy is motivated by the fact that MP is an idealized DCA algorithm. It assumes that a new call will be blocked only if there is no possible re-allocation of a channel to the call1 which would result in the call be carried. MP does not depend on any algorithm which implements the assignments of channels, and thereby provides the best performance a DCA scheme can possibly achieve in a given setting. Due to MP policy, a call will be accepted in cell Ci at time t provided ni−1 (t) + ni (t) ≤ M (1) ni+1 (t) + ni (t) ≤ M
(2)
are satisfied simultaneously after the call is accepted. If the above conditions are not satisfied, i.e., if either ni−1 (t) + ni (t) > M , or ni+1 (t) + ni (t) > M , by accepting the call, channel resource is going to be overloaded. The probability for such an event to occur is denoted as the overloading (O) probability Pi (t) at cell Ci at time t, i.e., (O)
Pi
(t) ≡ Pr({ni−1 (t) + ni (t) > M } ∪ {ni+1 (t) + ni (t) > M }). III. Call Admission Control Policy
We define our admission control policy to be consistent to that given in [5] but extended for dynamically assigned channels. Referring to Fig. 1, a new call is admitted to cell Ci at time t0 if and only if the following admission conditions are satisfied: 1. At the current time t0 , the number of calls in cell Ci and its adjacent cells will not exceed the total number of channels in the system. In other words, Equations (1) and (2) for MP strategy need to be satisfied at time t0 . This ensures that there is a channel available for the new call. If this condition is considered alone without QoS constraints, no QoS is enforced, and we end up with the original MP. 1 Including
re-allocating call in progress
2. At a future time t1 (= t0 + T ), the predicted overload probability of cell Ci is bounded by a given QoS threshold, i.e., (O) Pi (t1 ) ≤ PQoS , (3) where (O)
Pi
(t1 )
=
Pr({Ni−1 (t1 ) + Ni (t1 ) > M } ∪ {Ni+1 (t1 ) + Ni (t1 ) > M }).
Ni−1 (t1 )2 , Ni (t1 ), and Ni+1 (t1 ) stand for the number of users in cell Ci−1 , Ci , and Ci+1 at time t1 , respectively. Then some channels will be reserved for hand-off calls in the future. The number of channels reserved by the policy is not a constant, but determined by the number of users in cells Ci , Ci−1 and Ci+1 at time t0 . This ensures that QoS will be maintained in cell Ci . 3. The admission conditions for cell Ci−1 and cell Ci+1 can be stated similarly to the previous admission condition stated for cell Ci , i.e., (O)
Pi−1 (t1 ) ≤ PQoS ,
(4)
where (O)
Pi−1 (t1 )
=
and
Pr({Ni−2 (t1 ) + Ni−1 (t1 ) > M } ∪ {Ni (t1 ) + Ni−1 (t1 ) > M }). (O) Pi+1 (t1 )
≤ PQoS ,
(O)
(5)
Pr({Ni (t1 ) + Ni+1 (t1 ) > M } ∪ {Ni+2 (t1 ) + Ni+1 (t1 ) > M }).
A hand-off call is accepted by cell Ci if and only if Equations (1) and (2) are satisfied, which means a hand-off call is accepted whenever it is possible. Therefore, a hand-off call has higher proirity than a new call when applying for a channel. IV. Implementing The Admission Control Policy Two steps are needed to implement the admission control policy. One is to derive a QoS threshold PQoS . This includes relating PQoS with the desired blocking probability PBQoS and hand-off dropping probability PDQoS . Another is (O) (O) to evaluate the overload probabilities Pi−1 (t1 ), Pi (t1 ), and (O) Pi+1 (t1 ), respectively. These two steps, once completed, can be combined to make admission decisions. A. A QoS Measure for Admission Control with Dynamically Assigned Channels What should be an appropriate QoS measure (threshold) for the distributed admission control with dynamically assigned channels? We claim that a logical choice for PQoS is [10] PQoS =
α′ PBQoS + PDQ0S , α′ + 1
α′ =
1/h . (1/µ − 1/h)(1 − PBQoS )
PBQoS and PDQoS are the given QoS thresholds on the blocking and hand-off dropping probabilities. µ and h are the call hand-up rate and call hand-off rate, respectively. To examine whether such a QoS measure is meaningful, we consider two extreme cases. When PBQoS → 1, i.e., no constraint is enforced on the blocking probability, PQoS → 1. This simply means no QoS constraint is enforced. When PBQoS = 0, i.e., no call should be blocked, 1/h PQoS = PDQoS /( (1/µ−1/h) + 1). Since PQoS < PDQoS , if we choose a threshold PDQOS as the QoS threshold on the hand-off dropping probability alone, we would have a looser control over the desired QoS in general. However, when the hand-off happens more frequently than a new call arrival, 1/h ≈ 0. Then PQoS ≈ PDQoS . i.e., 1/h ≪ 1/µ so that (1/µ−1/h) In other words, the threshold PDQoS on the hand-off dropping probability alone is a good QoS measure (threshold) only when the desired blocking probability is very small and the hand-off occurs much more frequently than a new call arrival. B. Evaluating The Overload Probability
where Pi+1 (t1 ) =
3
where
The second step towards implementing the admission (O) policy is to evaluate the overload probabilities, Pi−1 (t1 ), (O)
(O)
Pi (t1 ) and Pi+1 (t1 ). Since these probabilities have a simi(O) lar form, we only need to evaluate Pi (t1 ). Using the model given in Section II, we can obtain an expression on the overload probability in a theorem below. Theorem 1: Let M be the number of channels in the system. Let ni (t0 ) be the number of users at cell Ci at time t0 . At time t1 (= t0 + T ), let Ni (t1 ) be the number of users in cell Ci . Define ∆Ni (t0 ) ≡ Ni (t1 ) − ni (t0 ) to be the number of users changed in cell Ci from time t0 to t1 . Then the overloading probability at cell Ci is Pr({Ni−1 (t1 ) + Ni (t1 ) > M } ∪ {Ni+1 (t1 ) + Ni (t1 ) > M }) =
M X
[Pr({∆Ni−1 (t0 ) > M − k − ni−1 (t0 )}) +
k=0
Pr({∆Ni+1 (t0 ) > M − k − ni+1 (t0 )}) − Pr({∆Ni−1 (t0 ) > M − k − ni−1 (t0 )}) · Pr({∆Ni+1 (t0 ) > M − k − ni+1 (t0 )})] · Pr(∆Ni (t0 ) = k − ni (t0 )). (7) The proof of the theorem can be found in [10]. Since the probabilities in each term of the above summation have a similar expression, we will only focus on evaluating Pr(∆Ni (t0 ) = k). Such a probability can be evaluated based on the given traffic model, and is given in a corollary below. Corollary 1: Pr(∆Ni (t0 ) = k) =
(6)
2 Random variables and constants are denoted by capital letters. Observed values are denoted by small letters.
(I)
e−[λi
(O)
(t0 )+λi
(t0 )]T
q
(I)
(O)
[λi (t0 )/λi q (I) (O) I|k|(2T λi (t0 )λi (t0 ) ).
(t0 )]k · (8)
4
where (I)
λi (t0 ) = (O)
λi
(t0 ) =
λi + [ni−1 (t0 ) + ni+1 (t0 )]
h , 2
ni (t0 )(µ + h).
Ik (x) is the modified Bessel function for all integer k ≥ 0. The proof of the corollary is given in [10]. Combining Equations (7) and (8), we have the expression (O) for the overloading probability Pi (t1 ) at cell Ci . The other two overloading probabilities can be obtained similarly. In general, these overloading probabilities can not be simplified to close forms. They are therefore evaluated numerically, and compared with the QoS threshold PQoS . If all three inequalities given in Equations (3), (4) and (5) are satisfied, a new call is admitted. Otherwise, the call is rejected.
PBQoS and PDQoS as explained in Section IV-A. If not, the actual QoS threshold set on the hand-off dropping probability is much smaller than it should be. This results in a very low hand-off dropping probability PD , and is undesirable, since the capacity is not being fully utilized. The hand-off dropping probability PD is almost the same as that for MP when PBQoS = 1.0. This is consistent to the extreme case we consider in Section IV-A, which means that the QoS is not enforced. When PBQoS = 0.2, DCA-QoS maintains the hand-off dropping probability PD to be close to PDQoS more consistently than FCA-QoS where PDQoS is being used alone [5]. C. Performance of DCA-QoS and FCA-QoS New call/Handoff call block/drop rates vs load
0
10
V. Numerical Results and Discussions
MP: dotted line FCA−QoS: dash line
−1
We use the same 1-D simulation system and the experimental set-up as in [5] to obtain our results for the purpose of comparison. The system consists of 10 cells arranged on a circle so that the boundary effect can be ignored. The number (M ) of distinguishable channels in the system is 40. We assume that the call duration (1/µ = 500s) is exponentially distributed. The time a call stays in a cell before handing off to another (1/h = 100s) is also exponentially distributed. We use the same performance measure as in [5], i.e., the new call blocking probability PB and hand-off dropping probability PD . The desired maximum tolerable hand-off dropping probability PDQoS is assumed to be 0.01. B. Testing The QoS Threshold PQoS Handoff call drop rate vs load
0
10
−1
Handoff Call Dropping Probability
10
−2
10
−3
10
−4
10
−5
10
−6
10
0
10
1
10 Erlang
2
10
Fig. 2. Comparison of QoS Threshold (PDQoS = 0.01). “− · −”: FCA-QoS; “—”: DCA-QoS (PBQoS = 0.2); “− − −”: DCAQoS (PBQoS = 1.0); “· · ·”: MP.
The first purpose of the experiments is to test the validity of the derived QoS measure. Fig. 2 compares the hand-off dropping probability PD among FCA-QoS, MP and DCAQoS under different QoS thresholds as used in [5]. When PQoS is chosen to satisfy PQoS = PDQoS , the hand-off dropping probability PD is much smaller than PDQoS . This is because that our QoS threshold (PQoS ) should include both
Call Blocking/Dropping Probability
10
A. Experimental Set-Up
DCA−QoS: solid line Handoff call: +
−2
10
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10
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10
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10
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10
0
10
1
10 Erlang
2
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Fig. 3. Comparison of DCA-QoS to FCA-QoS and MP: Uniform Traffic. Three curves from the top without “+”: new call blocking probability PB . Three curves with “+”: hand-off dropping probability PD .
The second purpose of the experiments is to access of the performance of the distributed admission control policy with DCA-QoS. The performance is compared with that of FCAQoS to understand how much more can be gained using DCAQoS compared with FCA-QoS. In particular, the performance of DCA-QOS is compared with that of MP and FCA-QoS. PBQoS = 0.2 and PDQoS = 0.01 are used to set our QoS threshold given in Equation (6), and PDQoS = 0.01 is used as the QoS threshold for FCA-QoS. The comparison of DCA-QoS to MP and FCA-QoS under uniform traffic is shown in Fig. 3. In terms of the blocking probability PB , the probability increases as the load for all three policies. MP always has the lowest blocking probability among the three policies, since no QoS is enforced to control the hand-off dropping probability. FCA-QoS has a higher PB than DCA-QoS. This is because that DCA makes more effective use of channels. In terms of the hand-off dropping probability PD , DCA-QoS always has the lowest value among the three policies. The hand-off dropping probability PD for MP goes up with the load, since no QoS is enforced for MP. For both FCA-QoS and DCA-QoS, PD saturates around the predefined value PDQoS . DCA-QoS always has a lower hand-off dropping probability PD than FCA-QoS. In other words, QoS is better maintained by DCA-QoS. We think the reason for this is that a Gaussian approximation is used to approximate
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TABLE I Comparison of Erlang load when the overloading probability
New call block rates vs load
0
10
MP: dotted line FCA−QoS: dash line −1
10
New Call Blocking Probability
is 0.01.
DCA−QoS: solid line Heavy traffic: +
Traffic patten Uniform Nonuniform (Light) Nonuniform (Heavy)
−2
10
−3
10
DCA-QoS 20.57 13.94 20.37
FCA-QoS 16.84 10.71 17.41
Gain (%) 22.15 30.16 17.00
−4
10
−5
10
0
1
10
10 Erlang
2
10
Fig. 4. Comparison of DCA-QoS to FCA-QoS and MP: Nonuniform Traffic. “—”: DCA-QoS; “− − −”: FCA-QoS; “· · ·”: MP; curves with “+”: Heavily-loaded; curves without “+”: Lightlyloaded.
the overloading probability for FCA-QoS, whereas a more accurate model is used to derive the overload probabilities in DCA-QoS. Handoff call drop rates vs load
0
10
MP: dotted line FCA−QoS: dash line DCA−QoS: solid line
−1
Handoff Call Dropping Probability
10
Heavy traffic: + −2
10
−3
10
and PDQoS = 0.01. We observed that DCA-QoS has consistently a higher capacity than FCA-QoS under both uniform and nonuniform traffic. In particular, comparing to FCAQoS, DCA-QoS has a gain in capacity from 17% to 30%. VI. Conclusion In this work, we have analyzed the performance of distributed admission control with dynamic channel allocation and QoS provisioning. We have first derived a novel QoS threshold which maintains the QoS on hand-off dropping probabilities consistently under both uniform and nonuniform conditions. We have then investigated DCA-QoS in such a way that a performance bound is provided on how well DCA can possibly do under the given QoS constraint in the given setting. We have found empirically that the capacity gain due to using DCA is 17% to 30% under various traffic conditions. Acknowledgment
−4
10
−5
10
−6
10
0
10
1
10 Erlang
2
10
The support from National Science Foundation ((CAREER) IRI-9502518) is greatly appreciated. Thank Sheng Ma for helpful discussions. References
Fig. 5. Comparison of DCA-QoS to FCA-QoS and MP: Nonuniform Traffic. “—”: DCA-QoS; “− − −”: FCA-QoS; “· · ·”: MP; curves with “+”: Heavily-loaded; curves without “+”: Lightlyloaded.
To compare the performance of DCA-QoS, MP, and FCAQoS under nonuniform traffic, the same simulation is used. The new call arrival rate is set to be the same every other cell so that the neighboring cells have a different new arrival rate, and the ratio is 2 between the heavy and the light load. Fig. 4 and Fig. 5 show the new call blocking probability PB and the hand-off call dropping probability PD of DCA-QoS, FCAQoS and MP under nonuniform traffic, respectively. Similar to the results under the uniform traffic, MP has the lowest PB and FCA-QoS has the highest PB in both lightly-loaded and heavily-loaded cells. Referring to Fig. 5, in lightly-loaded cells, PD has almost the same trend for both DCA-QoS and FCA-QoS. In heavily-loaded cells, however, DCA-QoS maintains a much better control on the hand-off dropping probability than FCA-QoS. Intuitively, this is due to the ability of DCA automatically adapts to traffic variations. To access how much has been gained by DCA-QoS compared to FCA-QoS in terms of the capacity, Table I compares Erlang load between DCA-QoS and FCA-QoS when PB = 0.2
[1]
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