Single server queuing model of Markov modulated bursty arrival with service following phase type distributions for underlay and overlay customers

Abstract

Among the waiting models proposed in the literature most of them focus on homogeneous arrival rate. This paper proposes a single server waiting line with modulated arrival rate of small and large size of traffic sources. Modulation of arrival rate induces the server to shift the service rate that follow phase type distribution. Using Neut’s versatile point process under quasi birth death environment we present the steady state analysis of the system. We provide examples numerically to perform the results and represent it in graphical form.

Keywords

• Markov modulated Poisson process
• Phase type distribution
• Quasi-birth–death process
• Matrix analytic method