MULTISERVER QUEUEING SYSTEM WITH MARKOVIAN ARRIVAL FLOW OF IMPATIENT CUSTOMERS OPERATING IN A RANDOM ENVIRONMENT

Abstract

Multiserver queuing system with an infinite buffer and impatient customers, operating in a random environment is investigated. Customers arrive to the system according to the Markovian arrival flow. Service time of a customer has a phase type distribution. During the waiting time in the buffer customers can be impatient and leave the system forever. The system parameters depend on the state of the random environment. The ergodicity condition is derived. The formulas for calculating the main performance measures of the system are obtained. The Laplace-Stieltjes transforms of waiting and sojourn times of a customer in the system are calculated.