Tandem queueing system MAP#x007C;M#x007C;N#x007C;K - N #x2192; #x25CF;#x007C;M#x007C;R#x007C;#x221E; with impatient customers as a model of remote technical support

摘要

We consider a tandem queueing system with Markovian Arrival Process (MAP) as a model of remote technical support. The first stage is a multi-server queueing system with a finite buffer and impatient customers. After the service at the first stage the customer leaves the system or moves to the second stage. The second stage has a finite number of servers and an infinite buffer. The service time at the first and second stages has an exponential distribution with different parameters. The ergodicity condition is derived. A numerically stable algorithm for calculation of the stationary distribution of the system under consideration is presented. The main performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn time distribution at the both stages are derived.