MINIMIZING LOSS PROBABILITY IN QUEUING SYSTEMS WITH HETEROGENEOUS SERVERS

Document Type: Regular Paper

Authors

1 Department of Statistic, Faculty of Arts and Sciences, Ondokuz Mayis University, Kurupelit, 55139-Samsun, Turkey,

2 Department of Statistic, Faculty of Arts and Sciences, Ondokuz Mayis University, Kurupelit, 55139-Samsun, Turkey

Abstract

The probability of losing a customer in M/G/n/0 and GI/M/n/0 loss queuing systems with
heterogeneous servers is minimized. The first system uses a queue discipline in which a customer who arrives
when there are free servers chooses any one of them with equal probability, but is lost otherwise. Provided
that the sum of the servers rates are fixed, loss probability in this system attains minimum value when all the
service rates are equal. The second system uses queue discipline, in which a customer who enters into the
system is assigned to the server with the lowest number. Loss probability in this system takes the minimum
value in the case when the fastest server rule is used in which an incoming customer is served by the free
server with the shortest mean service time. If the mean of the arrival distribution is fixed, then loss probability
is minimized by deterministic arrival distribution

Keywords