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On Single Server Queue with Batch Arrivals
Vitaly Sobolev
* 1 ,
Alexander Condratenko
2
1  Department of Probability Theory and Applied Mathematics; Moscow Technical University of Communications and Informatics
2  Faculty of Mechanics and Mathematics; Lomonosov Moscow State University
Academic Editor: Antonio Di Crescenzo
Published: 28 April 2023 by MDPI in The 1st International Online Conference on Mathematics and Applications session Probability and Statistics
https://doi.org/10.3390/IOCMA2023-14417
Abstract:

This paper deals with a queuing system with general renewal arrivals, exponential service times, single service channel and infinite number of waiting positions, customers are serviced in the order of their arrival. In the stationary case a new form of the probability generating functions of the number of clients in the system is derived. This new form is written in terms of the probability generating functions of the tail distribution function of the number of customers per group and of the probability generating functions of a embedded discrete time homogeneous Markov chain.

Keywords: queuing system; batch arrivals; stationary distribution; probability generating functions; embedded Markov chain
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Comments on this paper
Mike Alley
22 May 2023
The queueing literature has a long history of service systems with associated service durations. These systems have a wide range of applications, including logistics, industrial management, retro bowl and telecommunications.
Mike Alley
22 May 2023
Service systems with associated service durations have a long history in the queueing literature. These systems have a wide range of application domains, including logistics, production management, and telecommunications.retro bowl


 
 
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