Stationary distribution of an infinite-buffer batch-arrival and batch-service queue with random serving capacity and batch-size-dependent service

2021 ◽  
Vol 40 (1) ◽  
pp. 1
Author(s):  
S. Pradhan ◽  
U.C. Gupta
Keyword(s):  
Stationary Distribution ◽  
Batch Arrival ◽  
Batch Size ◽  
Batch Service ◽  
Size Dependent

scholarly journals Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
U. C. Gupta ◽  
S. Pradhan
Keyword(s):  
Joint Distribution ◽  
Probability Generating Function ◽  
Batch Size ◽  
Batch Service ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Size Dependent ◽  
Poisson Arrival ◽  
Bivariate Probability ◽  
Server Content

We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate probability generating function from which the joint distribution of queue and server content at departure epoch of a batch is extracted and presented in terms of roots of the characteristic equation. We also obtain the joint distribution of queue and server content at arbitrary epoch. Finally, the utility of analytical results is demonstrated by the inclusion of some numerical examples which also includes the investigation of multiple zeros.

scholarly journals Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

2013 ◽  
Vol 40 (5) ◽  
pp. 1497-1505 ◽  
Author(s):  
Dieter Claeys ◽  
Bart Steyaert ◽  
Joris Walraevens ◽  
Koenraad Laevens ◽  
Herwig Bruneel
Keyword(s):  
Batch Size ◽  
Batch Service ◽  
Queueing Model ◽  
Tail Probabilities ◽  
Size Dependent ◽  
Service Times

Optimal control of batch service queues

1973 ◽  
Vol 5 (2) ◽  
pp. 340-361 ◽  
Author(s):  
Rajat K. Deb ◽  
Richard F. Serfozo
Keyword(s):  
Decision Process ◽  
Time Horizon ◽  
Optimal Level ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Infinite Time ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Service Queues

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

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