On the BMAP_1, BMAP_2/PH/g, c retrial queueing system

TL;DR

This paper analyzes a complex retrial queueing system with Markovian arrivals and two customer types, deriving stability conditions, performance measures, and optimization strategies, and applying the model to cellular wireless networks.

Contribution

It introduces a novel analysis of a BMAP_1, BMAP_2/PH/g, c retrial queue using multi-dimensional asymptotically quasi-Toeplitz Markov chains, including stability and optimization methods.

Findings

Performance is mainly influenced by customer arrival and service patterns.

Retrial rate has a lesser impact on system performance.

Optimal server configurations can be determined through the proposed algorithm.

Abstract

In this paper, we analyze a retrial queueing system with Batch Markovian Arrival Processes and two types of customers. The rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process. Using the theory of multi-dimensional asymptotically quasi-Toeplitz Markov chain, we obtain the stability condition and the algorithm for calculating the stationary state distribution of the system. Main performance measures are presented. Furthermore, we investigate some optimization problems. The algorithm for determining the optimal number of guard servers and total servers is elaborated. Finally, this queueing system is applied to the cellular wireless network. Numerical results to illustrate the optimization problems and the impact of retrial on performance measures are provided. We find that the performance measures are mainly affected by the two types of customers' arrivals and service patterns, but the retrial rate plays a less crucial role.