Queuing analysis of polling models
ACM Computing Surveys (CSUR)
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Delay models for contention trees in closed populations
Performance Evaluation
Sojourn times in polling systems with various service disciplines
Performance Evaluation
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We analyse an M/G/1 queueing model with gated random order of service. In this service discipline there are a waiting room, in which arriving customers are collected, and a service queue. Each time the service queue becomes empty, all customers in the waiting room are put instantaneously and in random order into the service queue. The service times of customers are generally distributed with finite mean. We derive various bivariate steady-state probabilities and the bivariate Laplace–Stieltjes transform (LST) of the joint distribution of the sojourn times in the waiting room and the service queue. The derivation follows the line of reasoning of Avi-Itzhak and Halfin [4]. As a by-product, we obtain the joint sojourn times LST for several other gated service disciplines.