A queueing system with batch arrival of customers in sessions

This paper describes and analyzes a single-server queueing model with a finite buffer and session arrivals. Generation of the sessions is described by the Markov Arrival Process (MAP). Arrival of the groups of the requests within any admitted session is described by the Terminating Batch Markov Arrival Process (TBMAP). Service time of the request has Phase (PH) type distribution. The number of the sessions that can be simultaneously admitted to the system is under control.Analysis of the joint distribution of the number of sessions and requests in the system is implemented by means of the matrix technique. Analysis of the sojourn time of an arbitrary and admitted session is performed by means of the extension of the method of catastrophes. Effect of control on the main performance measures of the system is numerically demonstrated.

► A novel queueing model with session arrivals and group requests arrival is analyzed.
► Joint distribution of the number of requests and admitted sessions is computed.
► The sojourn time distribution of an arbitrary session is derived.
► The problem of optimization of the sessions admission strategy is discussed.
► Presented results are numerically illustrated.