On some parallels between the loss probability in the GI/G/1 loss system and the delay probability in the GI/G/1 queue

• Published in: Operations research letters Vol. 25; no. 4; pp. 191 - 194
• Main Author: Atkinson, J.Ben
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.1999
• Subjects: Delay probability; GI/G/1 loss system; GI/G/1 queue; Loss probability; Stochastic comparisons of queues; GI/G/1 queue; Stochastic comparisons of queues; Delay probability; GI/G/1 loss system; Loss probability
• ISSN: 0167-6377; 1872-7468
• DOI: 10.1016/S0167-6377(99)00044-9

In this paper, it is shown that the stationary probability of loss decreases when the service-time distribution becomes more variable in all H k /G/1 loss systems for k⩾2, while this probability increases when the service-time distribution becomes more variable in all GE 2/G/1 loss systems. These properties parallel those of the stationary probability of delay in the corresponding infinite-capacity GI/G/1 queues. The relationship between the loss probability in the E k /E l /1 loss system and the probability of delay in the E k /E l /1 queue is also discussed.