Optimal control of admission to a multiserver queue with two arrival streams

Abstract

Abstract-The problem of finding an optimal admission policy to an M / M / c queue with one controlled and one uncontrolled arrival stream is addressed in this paper. There are two streams of customers (customers of class 1 and 2) that are generated according to independent Poisson processes with constant arrival rates. The service time probability distribution is exponential and does not depend oil the class of the customers. Upon arrival a class 1 customer may be admitted or rejected, while incoming class 2 customers are always admitted. A statedependent reward is earned each time a new class 1 customer enters the system. When the discount factor is small, we show that there exists a stationary admission policy of a threshold type that maximizes the expected total discounted reward over an infinite horizon. A similar result is also obtained when considering the long-run average reward criterion. The proof relies on a new device that consists of a partial construction of the solution of the dynamic programming equation. Applications arising from teletraffic analysis are proposed.

A Call-Routing Problem with Service-Level Constraints

“…In the telecommunication literature, there are also routing control problems similar to the system described in this paper and, again, the models typically assume that Blanc et al (1992) describe a system in which type-L jobs arrive according to a Poisson process and are subject to admission control. Once admitted, type-L jobs queue together with type-H jobs, and the objective is to maximize a discounted total reward associated with the number of jobs accepted.…”

Effects of system parameters on the optimal policy structure in a class of queueing control problems

“…This is a simplified version of the model in [5], where all batches have unit sizes. Similar admission control problems for queueing systems have been studied by for instance Stidham [25] and Blanc et al [3].…”

Access control to two multiserver loss queues in series

“…There has been relatively little work done on admission control in loss networks, where the performance metric is a loss rate. Recently, Blanc [2] analyzed optimal control of admission to a multiserver queue with two arrival streams.…”

“…The lack of satisfactory theoretical results was perhaps partially responsible for the decline of interest in RLS-based DSTMV regulation for ARMAX plants, in favor of the more obvious (but numerically more demanding) approach relying upon modified extended RLS (see, e.g., [3]) or extended RLS (see, e.g., [2]). This is to be regretted because DSTMV regulation with RLS parameter estimation is a robust technique (see, e.g., [8]), easily accommodating all types of MV and pole-zero placement control laws for minimum phase as well as for nonminimum phase plants.…”

“…Its first broad exposition was presented by Goodwin and Sin (see [3]) and later developed by Chen and Guo (see, e.g., [2]). The main advantages of this approach are its fundamental nature, the power of already existing martingale theory, and the fact that both stability and convergence are analyzed simultaneously.…”