On estimates of the loss probability for an M/M/n queueing system with channels of different service productivity

Article type: Research Article

Authors: Puškorius, Stasys | Minkevičius, Saulius

Affiliations: Lithuanian Military Academy, Šilo 5a, 2055 Vilnius, Lithuania | Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. E-mail: mathematica.ktl.mii.lt

Abstract: The queueing system theory is well developed. Such an important problem as the efficient of customer service in efficiency a multichannel queueing system with different productivity of service channels is well developed, too. Exact formulas are obtained from which the loss probability can be computed (if the input stream of customers distributed as Poisson and service time of the customer is the exponential service time). However, these formulas are very complex. So, in this paper, two theorems are proved, in which upper and lower estimates of the loss probability are presented. These estimates are simple formulas that don't become more complex with the growing number of service channels in the queueing system.

Keywords: M/M/n queueing system, output stream of customers, the loss probability, upper and lower estimates of the loss probability

DOI: 10.3233/INF-1996-7306

Journal: Informatica, vol. 7, no. 3, pp. 361-370, 1996