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

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 Analysis of a versatile batch-service queueing model with correlation in the arrival process

2013 ◽  
Vol 70 (4) ◽  
pp. 300-316 ◽  
Author(s):  
Dieter Claeys ◽  
Bart Steyaert ◽  
Joris Walraevens ◽  
Koenraad Laevens ◽  
Herwig Bruneel
Keyword(s):  
Arrival Process ◽  
Batch Service ◽  
Queueing Model

An Uncertain Single-Server Queueing Model

2021 ◽  
pp. 2150001
Author(s):  
Kai Yao
Keyword(s):  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Queueing Model ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Service Efficiency ◽  
Service Times ◽  
Interarrival Times

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

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