On the Capacitated Loss Network with Heterogeneous Traffic and Contiguous Resource Allocation Constraints

Given a capacitated loss network, traffic arrivals with different bandwidth demands and reward rates (heterogeneous) -in the case that each traffic demand must be assigned in contiguous position, the problem is to find call admission/packing algorithms, such that the objective function (long-run average revenue) will be maximized. With contiguous allocation constraint, the First-Fit (FF) and Best-Fit (BF) policy simulation was examined, assuming Poisson arrivals with exponential holding time. The blocking probabilities from these two policies are compared with the Complete-Sharing (CS) policy and OptimalComplete-Partitioning (OCP) policy, which have no contiguous allocation concern. A loose optimal lower bound is obtained by using the theory of Semi-Markov Decision Processes (SMDP). The value-iteration algorithm is applied due to the huge cardinality of the system state space. Our systemic numerical study (among CS, FF, BF, OCP, SMDP policies) suggests that two novel heuristic admission/packing policies, Best-Fit with Reservation (BFR) and Moving Boundary First-Fit (MBFF), might have higher efficiency. INTRODUCTION The call admission and routing problem have been widely studied for variety of modern telecommunication networks. In this paper, the call admission/packing problem relates to the automation needs of the current SONET transport network switching. Due to hardware design limits, each traffic stream with a demand of STS-N must be allocated in the link contiguously once it is admitted, say, from n to N n + . Here, n is the start position of this traffic allocation in the link, and N n + is the end position of its allocation in this link. Therefore, the issue itself is not only a call admission problem, dealing with whether or not to accept a traffic arrival once it comes, but also a packing problem, dealing with where to put the traffic once it is decided to accept that traffic. This is an extremely complicated problem in the sense of obtaining the optimal solution. Even without admission control consideration, the packing problem (Dynamic Storage Allocation) itself is a NP hard problem [1]. Another research topic related to our problem is the call admission control in Multi-service loss systems ( flow control problem in telecommunication), which is widely studied in the ISDN system and ATM network literature up to the present time [2,3,4,5]. Our problem is an outgrowth of the flow control problem with an extra contiguous allocation constraint. Indeed, there are few references studying this problem. To simplify the slot assignment and tracking that are needed at both ends of the transmission system for ISDN, CCITT recommend that the time slots assigned to a broad band call should form one of the four pre-defined “channels” with six time slots each. V. Ramaswami, et al [6] have applied a Markov Process Model in a performance study of this problem in the case of two types of traffic arrivals, with the constraint that the wide-band calls are placed in fixedstarting-point contiguous regions of the channel and the narrow-band calls have to be packed. Although the performance analysis of this model is extremely complicated due to the explosion of the state space, it is clear that the problem in [6] is a special case of our call admission/packing problem. We give a systematic study of this problem. The SemiMarkov Process Model is applied to formulate the relaxed version of this problem, and the resulting optimal policy serves as the lower bound of our numerical study. First-Fit, Best-Fit, Optimal Complete Partitioning, as well as the well known Complete Sharing policies are studied under a variety of system parameters and traffic patterns. PROBLEM DEFINITION AND COMPLEXITY ANALYSIS Formally, the problem can be defined as follow: Given: Capacitated loss network, with capacity C on the link. Traffic demands, with k possible different bandwidth requirements k b b b , , , 2 1 K , and reward parameters k r r r , , , 2 1 L that is, there are heterogeneous traffic arrivals. Assume type-k traffic demand follows a Poisson process with mean arrival rate k λ , and the traffic holding time is exponentially distributed with mean 1/ k μ . Constraints: Each traffic demand must be assigned in contiguous position on the link. The total accepted traffic occupancy is no more than the link capacity C , i.e.,