The MAP/G/1/ Discrete-Time Queueing System with Inversive Service Order and Probabilistic Priority

This paper considers a discrete-time queueing system MAP∕G∕1∕∞ that is determined as follows. Upon arrival into the system of a new customer its length is compared with the (remaining) length of the customer in the device and with some probability which depends only on this two lengths, a new arrival will occupy the server while pushing out a servicing customer to the first place in the queue, and with the supplemental probability, alternatively, the newly arrived one occupies the first position in the queue (inversive service order and probabilistic priority). The main stationary characteristics of such systems behavior have been found. A number of numerical examples are presented according to found analytical formulae.

queueing system, discrete-time, inversive service order with probabilistic priority