For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. | Yugoslav Journal of Operations Research 22 (2012), Number 2, 285-296 DOI: APPROXIMATION OF THE STEADY STATE SYSTEM STATE DISTRIBUTION OF THE M/G/1 RETRIAL QUEUE WITH IMPATIENT CUSTOMERS Nadjet STIHI Laboratory LANOS, University of Annaba, Annaba, Algeria nstihi80@ Natalia DJELLAB Laboratory LANOS, University of Annaba Annaba, Algeria djellab@ Received: April 2011 / Accepted: April 2012 Abstract: For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints. Keywords: Retrial queue, steady state distribution, estimation, principle of maximum entropy, impatient customer. MSC: 60K25, 62G05, 54C70. 1. INTRODUCTION: MODEL DESCRIPTION The main characteristic of queuing systems with repeated attempts (retrial queues) is that a customer who finds the server busy upon arrival is obliged to leave the service area and join a retrial group (orbit). After some random time, the blocked 286 N. Stihi, N. Djellab / Approximation of the Steady State System State Distribution customer will have a chance to try his luck again. There is an extensive literature on the retrial queues and we refer the reader to [3], [7] and references there. The models in question arise in the analysis of different communication systems: cellular mobile networks, Internet, local area computer networks, see in [2], [4], [6]. In telephone networks, we can observe that a calling .
