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Optimization of Connection-Oriented, Mobile, Hybrid Network Systems Tamer A. ElBatt, Student Member, IEEE, and Anthony Ephremides, Fellow, IEEE

Abstract—In this paper, we consider the extension of a cellular system by means of satellite channels. Specifically, we consider an area covered by a number of cells, that is also covered by a number of spot beams. We consider connection-oriented service, and call durations are assumed to be exponentially distributed. Also, users are mobile and, as such, they may cross cell and/or spot-beam boundaries, thus necessitating handoffs. We incorporate the possibility of call dropping due to unsuccessful hand-off attempts, in addition to satellite propagation delays along with the probability of new call blocking, and formulate a specific multifaceted cost function that must be ultimately minimized. The minimization is to be carried out by choosing: 1) the optimal partitioning of channels between the cellular and the satellite systems, and ii) the call admission and assignment policy, subject to the constraints of a demand vector that consists of an exogenous (new-call) generation process and an internal (handoff-based) process that results from the mobility model. Two subproblems of this complex optimization problem are solved by means of numerical techniques and by means of so-called standard clock simulation techniques. In this solution method, we employ the ordinal optimization approach which focuses on preserving the performance rank, rather than the performance prediction of the different control policies. We find that the “double” coverage, through both cellular and satellite resources, results in substantial improvement over pure terrestrial or pure satellite systems for parameter values that correspond to practical environments. Index Terms— Blocking probability, call assignment, channel allocation, dropping probability, hybrid mobile networks, optimization.

I. INTRODUCTION

T

HE PROJECTED increase in the demand for mobile communication services requires efficient use of communication bandwidth. Land mobile satellite systems and terrestrial cellular networks are rapidly evolving to meet this demand. They were initially conceived as standalone systems (e.g., GSM and AMPS for terrestrial and the various LEO systems for satellite); recently, integrated (or hybrid) networks are being considered to support this surging demand. At first, these hybrid systems sought to extend the geographical coverage of the cellular system as shown in Fig. 1. However,

Manuscript received March 5, 1998; revised May 21, 1998. This work was supported by the Center for Satellite and Hybrid Communication Networks, a NASA Commercial Space Center (CSC), under NASA Cooperative Agreement NCC3-528. This paper was presented in part at the 17th AIAA International Communications Satellite Systems Conference, Yokohama, Japan, February 1998. The authors are with the Department of Electrical Engineering, University of Maryland, College Park, MD 20742 USA. Publisher Item Identifier S 0733-8716(99)01707-2.

Fig. 1. Hybrid mobile network [20].

the excess shared capacity in the satellite component of a hybrid system raises the possibility of utilizing it not only for providing “out-of-area” coverage to mobile users, but also for off-loading localized congestion in the underlying cells. In pure cellular networks, earlier studies have shown that efficient use of the system bandwidth can be achieved by reuse partitioning [1] and by using hierarchical cell layout [2], [3] with larger macrocells overlaying a collection of small microcells. The problem of finding the optimal partition of the frequency spectrum between microcells and macrocells was also addressed in [4]. However, the call assignment policy was assumed to be speed dependent. In [5], the performance analysis of a hierarchical cellular mobile communication system was introduced. The call assignment policy was assumed to be speed dependent in this work too. The performance analysis of a hybrid satellite–cellular system with the satellite footprints forming the highest layer in the hierarchy has also been studied [6]. However, according to the model proposed in that study, the call assignment policy used had fewer degrees of freedom than the ones investigated here. Moreover, the bandwidth partitioning was assumed to be known. In [7],

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integration of a multispot satellite system in the EHF frequency band with terrestrial cellular systems was investigated. A channel model was introduced for the satellite link, which is affected by propagation effects, environmental effects, and cochannel interference. Handover procedures for hierarchical cellular networks were proposed and analyzed in [8] and [9]. This work builds upon earlier work [10] in which users’ mobility, handoffs, and call assignment policy were not considered, but rather only a static split of the total number of channels into a terrestrial and a satellite component. In this paper, we use standard simple mobility models that permit us to evaluate the need (and probability) of handoffs. We consider the problem of minimizing the probability of blocking call requests while, at the same time, we are interested in keeping the propagation delay and call-dropping probability as small as possible. Hence, an arriving call that is assigned to a satellite channel will incur longer propagation delay, but may contribute to reduced overall blocking probability. More specifically, we introduce a multidimensional Markov chain-based model for a simple hybrid network consisting of two cells overlaid by one spot beam which can be extended to a larger system having any number of cells and spot beams in future work. We intentionally limit our attention to the very simple, single-footprint, two-cell system in order to better understand the tradeoff between the satellite and the terrestrial resources. We believe that this tradeoff is expected to remain valid even for a larger number of cells and spot beams reflecting practical network setups. In this work, we are not addressing terminal design and antenna or switch complexities, but rather system design issues and performance evaluation. Our main objective is to determine the optimal channel partitioning between the cellular and the satellite systems, as well as deciding the optimum call assignment policy, in order to minimize a multifaceted cost function composed of the call-blocking and dropping probabilities, in addition to the satellite propagation delays. For the optimization problem, we use the concept of ordinal optimization proposed in [11] as an approach to find a “good,” although not necessarily optimal, solution. This optimization concept aims at the determination of policies that perform relatively well compared to other candidate policies, without necessarily obtaining accurate estimates of the performance values associated with these policies. Frequently, a simplification of the otherwise complex optimization problem preserves the performance ranking among candidate policies quite well, and thus is an appropriate tool when accurate performance prediction is not required. We also make use of the improved efficiency achieved via using standard clock (SC) simulation [12] which permits the simultaneous evaluation of system performance under a large number of control policies. In the literature, various approaches have been considered for ordinal optimization [13]. In this paper, short simulation runs arrival events) were employed in conjunction with SC ( simulation to obtain approximate ranking of policies. We observed that many of the high-performance policies also arrival events), perform well over long simulation runs ( and thus justify the use of the ordinal optimization approach for solving our problem.

Fig. 2. Hybrid mobile network of two cells and one spot beam.

This paper is organized as follows: In Section II, the system description and the mathematical framework are given. Candidate call assignment policies are introduced in Section III. This is followed by the optimization problem formulation in Section IV. Next, the optimization approach is illustrated in Section V. In Section VI, numerical and simulation results for various subproblems are given and discussed. Finally, the conclusions are drawn in Section VII. II. HYBRID MOBILE NETWORK MODEL A. Assumptions In order to investigate the joint channel partitioning and call assignment optimization problem, we first make the following assumptions and introduce appropriate notation. The network and in addition under consideration consists of two cells to one spot beam “ ” covering the same area as shown in according to a Poisson Fig. 2. New calls arrive at cell , 2. The duration of arrival process with rate calls/min, each call is exponentially distributed with mean 1/ min. The total number of predesign channels available to the system is , where

and , , and are the number of channels dedicated to , , and , respectively. The two base stations, namely and , can communicate via either a terrestrial wireline connection or a wireless gateway located on the border between the cells. In this formulation, the wireless gateway assumption is made so that the model can be extendable to the case of mobile BS’s in the future. It does not affect in a substantial way the tradeoff though. According to this assumption, a mobile-to-mobile call originating in a cell and destined to the other cell needs four duplex channels if served terrestrially by the cellular network. A mobile user can alternatively access the satellite directly (not through its BS) using a dual-mode satellite/cellular mobile terminal [14]. All call types have the same priority, and all calls considered in the model are mobile-to-mobile calls. BS’s and spot beams are assumed to be stationary. We define to be the fraction of calls originating in one cell and destined to the ). When mobiles, served terrestrially, other cell ( reach the cell boundaries, the call could be handed off either

ELBATT AND EPHREMIDES: OPTIMIZATION OF CONNECTION-ORIENTED NETWORK SYSTEMS

to the neighboring cell or to the overlaying spot beam. In this formulation, call handoffs are assigned either to the neighboring cell or to the overlaying spot beam according to the same assignment rule used for new calls. The interhandoff is exponentially distributed with time for a mobile in cell min, , 2. Finally, we assume that blocked mean 1/ calls are cleared.

375

we define the sets

B. Markov Chain Formulation The state of the system can be defined by the vector , , , where number of calls of type “11,” that is, calls served by and both parties are in ; number of calls of type “12,” that is, calls served by and , where one of the parties is in and ; the other is in number of calls of type “22,” that is, calls served by and both parties are in ; number of calls of type “ ” that is, calls served by . Accordingly, the system is modeled as a four-dimensional continuous-time Markov chain. It should be noticed that calls of type “12” need four channels/call, while calls of types “11,” “22,” and “ ” need only two channels/call. If we had assumed that the terrestrial cells are connected, not via a wireless gateway, but via a terrestrial wired one, all call types would require two channels each. Therefore, the set of feasible states should satisfy the following constraints:

Then

provided . Similarly, the dropping probabilities of call handoffs , , , and are given by

(1) The vector of steady-state probabilities , consisting of the as varies through the state space defined values of by (1), can now be determined by solving the global balance equations written in the following matrix form:

(2) where is the state transition rate matrix and is the number of states in the state space that follows from (1). The entries are determined by the assumed rates of call arrivals, in terminations, and handoffs, as well as by the call assignment , , ) changes to policy. For example, state ( , , , , ) if a new call having both parties in is ( . This happens with a certain generated and is assigned to rate if the call assignment policy assigns this new call to the terrestrial cells provided the state is within the interior of the state space. Thus, the determination of all entries in is quite an elaborate process. In Section III, we provide more details. and The average blocking and dropping probabilities can be determined from the vector of steady-state probabilities as follows. First, the call-blocking probability for each call type, , , and , can be computed. To this end, namely,

The reason that the latter two dropping probabilities are zero is that when a mobile from cell “ ” is already served terrestrially ) moves to cell “ ,” there are for a call to cell “ ” ( already adequate resources in that call to handle this new type of call because of the assumed wireless gateway. This would not be the case if the intercell connection were via a wired terrestrial infrastructure. III. CALL ASSIGNMENT POLICIES HYBRID MOBILE NETWORK

FOR A

In this section, we address the problem of assigning a new incoming call or a handed-off call to the terrestrial cellular network or to the satellite. Two simple deterministic assignment rules based on complete sharing have been investigated in [10], namely, the cellular first (CF) assignment policy and the satellite first (SF) assignment policy. The authors have shown that the CF policy outperforms the SF policy, and explained it relying on the fact that the satellite capacity in a beam is shared by all of the users in the footprint of that beam. Here, we extend the class of assignment rules to include more general randomized rules. Any call, either new or handed

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off, is assigned according to the outcome of a coin flipped either to the terrestrial cellular network or to the satellite, provided that they both have available resources. The call is blocked only if no resources are available in both layers. The call assignment probabilities can be chosen to depend on the call types since different call types generally have different channel requirements and hand-off rates. This allows more degrees of freedom in the optimization problem. The question that arises next is how the call assignment is performed at the state-space boundaries where one of the two layers is filled up while the other still has resources. Clearly, the assignment rule has to be switched to a deterministic one to make full use of the available resources. Two switching boundaries are introduced next: switching at the state space boundaries, and switching at threshold boundaries.

State-space boundaries:

A. Switching at the Space Boundaries Under this class of policies, in the interior of the state space, a new incoming call or a handed-off one is assigned either to the terrestrial layer or to the satellite layer randomly based on assignment probabilities for each call type. For the network shown in Fig. 2, the call assignment probabilities are given by probability of assigning a call, with both parties , to cell ; in probability of assigning a call, with both parties , to spot beam ; in probability of assigning a call, with one of and the other in , to the the parties in and ; terrestrial resources, namely, to cells probability of assigning a call, with one of the and the other in , to spot beam parties in ; probability of assigning a call, with both parties , to cell ; in probability of assigning a call, with both parties , to spot beam . in When the system reaches the space boundaries due to a , , while spot beam still fully occupied cell has free channels, the assignment procedure switches from the randomized mode to a deterministic mode where the incoming calls or the handed-off ones are assigned immediately to the satellite . By the same argument, if the system reaches the space boundaries due to a fully occupied spot beam, while the terrestrial layer still has free channels, call handoffs or new call arrivals are assigned immediately to the terrestrial cellular network. In the following, we show a sample of the state transition rates that constitute the state transition rate matrix . The set of states in the state space defined by (1) can be divided into the following subsets. Interior of the state space:

The state transition rate out of state , , , to state , denoted by , depends on the position of within the state space. For instance, let us consider state (sample of the state-space interior). the state For new call arrival events, we have

For call completion events, we have

And finally, for call handoff events, we have

On the other hand, consider (i.e., a state on the statespace boundaries). The state transition rates will be given by the following.

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377

s.t.

For new call arrival events, we have

and for call hand-off events, we have

where

. Likewise, the state transition rates out of states in the remaining subsets can be determined in a similar fashion. B. Threshold Boundary Switching This class of assignment rules is motivated by the following considerations: 1) A call of type “12” needs four channels if served terrestrially, and only two channels if served by the satellite 2) Dropping an ongoing call is more severe than rejecting a new one. Thus, assignment policies that switch at boundaries within the original state space need to be examined. In general, we should study switching the assignment rule at the boundaries of all possible subspaces. In this paper, we consider examining a special type of boundaries, namely, threshold boundaries. The reason for this is that prior experience [19] shows that classes of policies with threshold boundaries can perform close to overall optimal policies in general Markov decision problems like the one we consider here. So under this class of policies, we enable switching from the randomized rule to a deterministic rule (for new calls) upon /2, /2, and /2 on the number reaching the thresholds of calls of types “11,” “12,” and “22,” respectively, as follows: if if if

average new call-blocking probability; average call-dropping probability; average percentage of satellite calls in the system (this represents the consideration of the satellite propagation delay in the optimization problem) and are weighting factors that are chosen to reflect and the desired relative importance of the different components in the cost function. In the above formulation, the choice of the parameters and is rather unguided since there is no well-defined procedure for choosing them. The following formulation is equivalent and easier to implement. It consists of minimizing one component of the composite cost function above subject to the other components staying below predetermined acceptable thresholds, namely, (4) s.t.

The quantities and are the alternative (equivalent) parameters in a one-to-one correspondence to the values of and , respectively. In the following, we consider decomposing the overall optimization problem into simpler subproblems, each of which addresses one aspect of the overall, original problem. The reason we choose to do so is the sheer complexity of the overall problem. A. The Optimum Channel Partitioning for a Given Assignment Rule

where

, and and employing the first call Given assignment rule in Section III, the objective is to solve the following minimization problem: (5) IV. THE OPTIMIZATION PROBLEM

The optimal call assignment strategy, that switches at the space boundaries, and the optimal channel partitioning policy are obtained from the following minimization problem: (3)

s.t.

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Usually, Markov decision and optimization problems of this type benefit from the existence of product-form solutions that permit a relatively efficient computation of the state probabilities for small-size problem instances, and that permits the use of analytical optimization techniques. However, here, the product-form solution is not applicable since the fourdimensional Markov chain does not satisfy the detailed balance equations and is hence irreversible [16]; the reason is that the call assignment rule switches at the space boundaries. For large state spaces, simulation is the only feasible way to measure the system performance for each policy and then rank them for deciding optimality. B. The Optimum Call Assignment for a Given Channel Partitioning According to Section III, two call assignment policies were to be investigated, namely, switching from a randomized assignment rule to a deterministic rule at the space boundaries, and at threshold boundaries within the original state space. and , 1) Switching at the Space Boundaries: Given the objective is to solve the following minimization problem: (6)

s.t.

For the same reasons as before, the only way to perform this optimization is to resort to simulation and to the subsequent ranking of the candidate policies. 2) Switching at Threshold Boundaries: Given , and , the objective is to solve the following minimization problem: (7)

s.t.

Again, here, the underlying Markov chain is irreversible, and hence, the global balance equations can only be solved numerically. For larger state spaces, of course, the only feasible method is resorting to simulation.

V. OPTIMIZATION APPROACH As presented in the previous section, the complex problem of jointly optimizing the channel partitioning and the call assignment policy was decomposed to the following subproblems: (channel partitioning) for a 1) determining given assignment rule, (assignment rule) for given 2) determining 3) refining the assignment rule by optimizing over threshold boundaries. The formulation of the aforementioned subproblems can be solved via discrete exhaustive search. Accordingly, the optimization problem solution consists of the following two components. a) Numerical Solution Component: The global balance equations were solved (using Mathematica 3.0) for the system steady-state probabilities under each policy. Thus, the call-blocking and dropping probabilities can be determined and compared. This approach becomes extremely complex very quickly in response to any increase in the size of the problem (i.e., the dimensionality of the Markov chain), and thus is not practical. This is especially aggravated by the lack of a product-form solution. b) Simulation Component: A simulation process was developed using C++ and run on a Sun-Ultra1 workstation. To increase the efficiency of the simulation, we used the so-called standard clock (SC) simulation method. In [12], the principles of SC simulation are explored in detail. Its basic value is that it permits the simultaneous measurement of the performance of multiple different control policies with a single simulation run. The improved efficiency of the SC method is achieved by using a sequence of (interevent time, event type) pairs, known as the clock sequence, to simultaneously generate sample paths for a number of structurally similar, but parametrically different, systems. Hence, each event generated is passed to all sample paths under investigation. This has a dramatic effect on the overall simulation time since the generation of events is considerably more time consuming than updating the system state. Moreover, as we are more interested in the relative ranking of policies rather than in their actual performance values, and to further speed up the simulations, ordinal optimization was employed. Ordinal optimization is the determination of control policies that perform relatively well compared to other candidate policies without necessarily obtaining accurate estimates of the performance values associated with these policies. The motivation underlying ordinal optimization is that finding the optimal solution (policy) is often too expensive or time consuming, although a suboptimal solution (that may be found quite easily) may provide sufficiently good performance. Moreover, it is not necessary to obtain accurate estimates of system performance values associated with these policies if an accurate ranking of these policies can be determined.

ELBATT AND EPHREMIDES: OPTIMIZATION OF CONNECTION-ORIENTED NETWORK SYSTEMS

TABLE I SYSTEM PARAMETERS Total Predesign Bandwidth (M) Call arrival Rate Per Cell () Call Service Rate () Call Handoff Rate from C1 (h ) Call Handoff Rate from C2 (h ) Fraction of Calls Originating in a Call and Destined to the Other Cell (f)

TABLE II CHANNEL PARTITIONING POLICIES 8 channels 0.33 calls/min 0.33 calls/min 0.5 calls/min 0.5 calls/min 0.5

Ordinal optimization has been applied using several approaches, namely, short simulation runs, crude analytical models, and imprecise simulation models [13]. The common observation among these approaches was that, although the measured performance may not be very accurate, the ranking of policies was relatively unaffected. In this paper, ordinal optimization based on short simulation runs was implemented based on SC simulation results. Of course, there was no a priori assurance that in our problem ordinal optimization would be applicable. As in all cases, ordinal optimization is here, too, a heuristic that must be tested. Fortunately, our results showed that it applies very satisfactorily since the ordinal ranking of the different candidate policies under fast and efficient simulations was largely the same as the exact (accurate) ranking (determined via long simulations). VI. NUMERICAL

AND

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SIMULATION RESULTS

The network shown in Fig. 2 was analyzed assuming the numerical parameters given in Table I. It should be pointed out here that the following results were obtained with no or while minimizing unless constraints enforced on and were assumed to be 1 in (4). otherwise stated, i.e., Considering the first subproblem, the optimum channel partitioning for a given call assignment policy was determined for the following call assignment probabilities:

Recall that each mobile-to-mobile call needs two-duplex channels per cell or spot beam. Hence, the set of channel allocation policies to be examined can be restricted to 15 , , and . different policies having even values for Furthermore, the channel partitioning policies investigated were further restricted to only nine policies, given in Table II, due to the symmetry of the parameters associated with cells and . Therefore, the two policies and had exactly the same performance. In Fig. 3, the call-blocking and dropping probabilities obtained numerically and via SC simulation were noticed to have good agreement for all channel partitioning policies. Moreover, the optimum channel partitioning policy turned out to be the all-channels-to-satellite policy ( ) since no constraints were enforced on the dropping probabilities or the propagation delays. If the satellite propagation delay is considered in the optimization problem, the all-channels-to-satellite policy is expected to have a higher cost depending on the weight associated with the propagation delay relative to the call-blocking probability. Later in this

Channel Partitioning Policy Policy Policy Policy Policy Policy Policy Policy Policy Policy

#1 #2 #3 #4 #5 #6 #7 #8 #9

M1 M2 Ms 0 2 2 2 4 4 2 6 8

0 0 2 4 0 4 6 0 0

8 6 4 2 4 0 0 2 0

section, we show that the optimum channel partitioning policy differs from the above mentioned one if a constraint is imposed on the satellite propagation delay. In Figs. 4 and 5, ordinal rankings based on call-blocking and dropping probabilities were plotted for simulation runs of various lengths versus the exact ranking obtained numerically. It was noticed that short simulation runs, while giving inaccurate call-blocking and dropping probabilities, retain the correct ordinal ranking of the best policies. In Fig. 6, the same channel partitioning policies investigated earlier were compared for their average blocking probability, average dropping probability and average percentage of satellite calls (representing the consideration of satellite propagation delay). Thus, the multifaceted cost function was optimized by enforcing upper bounds on two optimization criteria, and then minimizing the third subject to these constraints. For and : instance, if we impose the following constraints on

it can be obtained from Fig. 6 that the minimum value of is 0.29 and is achieved by policy 4 (i.e., ). Accordingly, it can be concluded that splitting the available number of channels into terrestrial and satellite components minimizes the multifaceted cost function as compared to the two extremes, namely, pure cellular and pure satellite systems. For the second subproblem formulated in Section IV, two assignment policies have been studied for a given channel partitioning policy. First, the problem formulated in (6) was solved for the optimum call assignment probabilities given the following channel partitioning:

The call assignment probabilities can take any value in the range [0, 1], leading to an infinite pool of call assignment policies. We have chosen a finite subset of policies that cover the whole range. Initially, a large subset (1331 policy) was arrival events chosen. The solution via SC simulation with within this subset was infeasible due to the very long simulation time incurred. Therefore, the set was reduced to a smaller one (64 policies) covering the [0, 1] range, which required a reasonable simulation time. The ranking of policies based on blocking and dropping probabilities generated by various

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Fig. 3. Blocking and dropping probabilities for channel allocation policies (numerical and simulation results).

simulation lengths are shown in Figs. 7 and 8, respectively. It can be noticed from Fig. 7 that the blocking trajectory for 10K arrival events has a wider performance range between best and worst policies than the one associated with 1 M arrival events. Furthermore, by increasing the simulation length, this range shrinks monotonically. Therefore, given the small performance range between extreme policies, the following simple call assignment policies are worth being examined. 1) Cellular First (CF) Assignment Policy ( ): This policy had a blocking-probability-based ranking of 29 out of the 64 policies investigated, and a dropping-probability-based ranking of 17. 2) Satellite First (SF) Assignment Policy ( ): It had a blocking-probability-based ranking of 44 out of 64, and a dropping-probability-based ranking of 63. From the above results, two observations can be pointed out. First, the CF policy outperforms the SF policy (with respect and ), which can be explained by recalling that to the satellite capacity in a beam is shared by all of the cells overlaid by that beam. So, when localized congestion occurs in a particular cell, i.e., its cellular channels fill up, then under the CF policy, some satellite channels may still be free to off-load the congestion, while under the SF policy, no free channels are available, as they are also being used by calls from cells with no congestion. Second, the CF policy gave , ) blocking and dropping rates ( that are not much inferior to those achieved by the optimum ). Hence, since the CF policy ( policy is easy to implement, it can be considered a suboptimal call assignment policy for this hybrid mobile system. On the other hand, the problem formulated in (7) has been solved for the optimum switching thresholds given that

the total number of predesign channels along with the following channel partitioning and call assignment probabilities:

From the constraints of (7), the set of threshold policies , , and is restricted to those having even values for . Consequently, the threshold policies examined are given below: 1) 2) 3) 4) 5) These policies are compared with the case of switching at the state-space boundaries in Table III. From Table III, it can be noticed that for the given channel partitioning, the call assignment probabilities, and the system numerical parameters, switching from the randomized assignment rule to a deterministic rule at appropriate thresholds improves the call-dropping probability as compared to the case of switching at the original state-space boundaries. This is achieved at the expense of increasing the new call-blocking probability. Therefore, with the assumption that dropping an ongoing call is less desired than blocking a new one, this assignment strategy proposes an approach for controlling the relative importance of the blocking and dropping rates.

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(a)

(a)

(b)

(b)

(c)

(c)

Fig. 4. Ordinal rankings based on blocking probabilities for channel allocation policies. (a) 10K arrival events. (b) 100K arrival events. (c) 1 M arrival events.

Fig. 5. Ordinal rankings based on dropping probabilities for channel allocation policies. (a) 10K arrival events. (b) 100K arrival events. (c) 1 M arrival events.

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Fig. 6. Simulation-based call blocking, dropping, and propagation delay performance for the channel allocation policies.

Fig. 7. Call-blocking probabilities for call assignment policies ranked based on SC simulations of different lengths.

VII. CONCLUSIONS In this paper, we considered the problem of optimizing the channel partitioning and call assignment policy for a hybrid mobile network. The objective was to minimize a multifaceted

cost function composed of the call-blocking and dropping probabilities in addition to the satellite propagation delays. For the subproblem of optimizing the channel partitioning given a call assignment policy, we observed that short simulation runs retain the correct ordinal ranking of most policies (certainly

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Fig. 8. Call-dropping probabilities for call assignment policies ranked based on SC simulations of different lengths.

REFERENCES

TABLE III SWITCHING POLICIES Switching Policy Switch at the original state space boundaries

11 8, 12 = 0, 22 = 8

11 = 6, 12 = 2, 22 = 6

11 = 4, 12 = 4, 22 = 4

11 = 2, 12 = 6, 22 = 2

11 = 0, 12 = 8, 22 = 0

=

Pb

Pd

0.0076 0.1887 0.072 0.0268 0.0448 0.174

0.0025 0.0003 0.0009 0.0015 0.0012 0.0001

of the optimum ones). Furthermore, the optimum channel partitioning turned out to be the all-channels-to-satellite policy if the blocking probability was the only optimization criterion. On the other hand, if the satellite propagation delay was considered in the optimization problem, the hybrid system was found to be the optimum as compared to the pure cellular network and pure satellite network extremes. Next, the subproblem of optimizing the call assignment policy given a channel partitioning was solved. For the switching at the space boundaries assignment strategy, it was noticed that the performance range between extreme policies was small. Accordingly, the simple cellular first assignment policy can be considered a near-optimal assignment rule. On the other hand, the call assignment rule of threshold boundary switching was examined. It was noticed that this policy can reduce the call dropping rate at the expense of a tolerable degradation in the blocking rate. Therefore, this assignment strategy permits more flexible handling of the relative importance of the blocking and dropping probabilities.

[1] J. Zander, “Generalized re-use partitioning in cellular mobile radio,” in Proc. Veh. Technol. Conf., May 1993, pp. 181–184. [2] J. Zander and M. Frodigh, “Capacity allocation and channel assignment in cellular radio systems using re-use partitioning,” Electron. Lett., vol. 28, pp. 438–440, Feb. 1992. [3] C. Lin, L. Greenstein, and R. Gitlin, “A microcell/macrocell cellular architecture for low and high mobility wireless users,” IEEE J. Select. Areas Commun., vol. 11, pp. 885–891, Aug. 1993. [4] K. Yeung, and S. Nanda, “Channel management in microcell/macrocell Cellular radio systems,” IEEE Trans. Veh. Technol., vol. 45, pp. 601–612, Nov. 1996. [5] L. Chin and J. Chang, “Performance analysis of a hierarchical cellular mobile Communication system,” in Proc. Int. Conf. Universal Personal Commun., 1993, pp. 128–132. [6] L. Hu and S. Rappaport, “Personal communication systems using multiple Hierarchical cellular overlays,” IEEE J. Select. Areas Commun., vol. 13, pp. 406–415, Feb. 1995. [7] C. Caini, G. Corazza, G. Falciasecca, M. Ruggieri, and F. Vatalaro, “A spectrum and power-efficient EHF mobile satellite system to be integrated with terrestrial cellular systems,” IEEE J. Select. Areas Commun., vol. 10, pp. 1315–1324, Oct. 1992. [8] R. Beraldi, S. Marano, and C. Mastroianni, “Performance of a reversible hierarchical cellular system,” Int. J. Wireless Inform. Networks, vol. 4, pp. 43–54, Jan. 1997. [9] G. Corazza, M. Ruggieri, F. Santucci, and F. Vatalaro, “Handover Procedures in Integrated Satellite and Terrestrial Mobile Systems,” 1994. [10] D. Ayyagari, “Blocking analysis and simulation studies in satelliteaugmented cellular networks,” Master’s thesis, Univ. Maryland, College Park, 1996. [11] Y. Ho, R. Sreenivas, and P. Vakili, “Ordinal optimization of DEDS,” J. Discrete Event Dynamic Syst., vol. 2, pp. 61–88, 1992. [12] P. Vakili, “Using a standard clock technique for efficient simulation,” Oper. Res. Lett., vol. 10, pp. 445–452, 1991. [13] J. Wieselthier, C. Barnhart, and A. Ephremides, “Ordinal optimization of admission control in wireless multihop integrated networks via standard clock simulation,” Naval Res. Lab., NRL/FR/5521-95-9781, 1995.

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[14] E. Drucker, P. Estabrook, D. Pinck, and L. Ekroot, “Integration of mobile satellite and cellular systems,” Jet Propulsion Lab. Tech. Rep., 1994. [15] D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1987 (2nd ed., 1992). [16] K. Ross, Multiservice Loss Models for Broadband Telecommunication Networks. New York: Springer-Verlag, 1995. [17] F. Kelly, Reversibility and Stochastic Networks. New York: Wiley, 1979. [18] S. Ramseier and A. Ephremides, “Admission control schemes for spotbeam satellite networks,” J. High Speed Networks, vol. 5, pp. 73–86, 1996. [19] S. Jordan and P. Varaiya, “Control of multiple service, multiple resource communication networks,” IEEE Trans. Commun., vol. 42, pp. 2979–2988, Nov. 1994. [20] D. Ayyagari and A. Ephremides, “Blocking analysis and simulation studies in satellite-augmented cellular networks,” in Proc. 7th IEEE Int. Symp. Personal, Indoor and Mobile Radio Commun., PIMRC’96, vol. 2, 1996, pp. 437–441. , “A satellite augmented cellular network concept,” Wireless [21] Networks, to be published.

Tamer A. ElBatt (S’98) received the B.Sc. degree with honors and the M.Sc. degree, both in electrical engineering, from Cairo University, Giza, Egypt, in 1993 and 1996, respectively. He is currently working toward the Ph.D. degree at the University of Maryland, College Park, where he has been a Graduate Research Assistant with the Center for Satellite and Hybrid Communication Networks since August 1996. From 1993 to 1996, he was a Teaching Assistant at Cairo University. His research interests lie in the general areas of design of mobile networks, satellite/cellular integrated networks, performance analysis, and optimization.

Anthony Ephremides (S’68–M’71–SM’77–F’84), for a photograph and biography, see this issue, p. 131.