Analytical Investigation of a Single-Server Queueing System with an Incoming MAP Event Flow

This paper considers a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow with two states. Explicit expressions are derived for the stationary probability distribution of the states and several numerical characteristics of the system (the probability of idle time of the server, the expected number of requests in the system, and the mean queue length). The resulting numerical characteristics are presented in tables and plotted in graphical form as well. The recurrent MAP flow with two states as a special case of correlated MAP request flows is studied.

Automated summary

This study focuses on a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow consisting of two states. The paper derives explicit expressions for the stationary probability distribution of the states and evaluates several numerical characteristics of the system, including the probability of idle time for the server, the expected number of requests in the system, and the mean queue length. Results are presented in tabular and graphical form, and the paper also examines the recurrent MAP flow as a special case of correlated MAP request flows.