A Multi-server Queueing Model with Markovian Arrivals and Phase Type Cooperative Services - Simulation Approach

Abstract

In Chakravarthy [5] a new class of queueing models in which one type of customers opt for cooperative services with fellow customers was introduced in the context of a single server. Under the assumption of versatile Markovian point process for the arrivals, exponential services, and with a limit of no more than two groups of cooperative customers be present in the system, the model was analyzed in steady-state and some interesting numerical examples were illustrated in [5]. In this paper we generalize that cooperative services model by relaxing the assumptions of single server, exponential services, and only two groups be present at any given time. Thus, we consider a multi-server queueing model in which the customers arrive according to a versatile Markovian point process. One type of customers require individual services whereas the second type of customers opt for a cooperative service (to be offered along with other similar customers). We assume that at any given time there can be at most \(K, 2 < K \le \infty \), groups of customers needing cooperative services and that the services are of phase type with representation depending on the type of service offered. While this model can be analyzed using matrix-analytic method with a very large state space, in this paper we will study the model using simulation to bring out a few salient features of this new class of queueing models.