Informatics and Applications
2020, Volume 14, Issue 4, pp 25-32
STATIONARY CHARACTERISTICS OF DISCRETE-TIME Geo/G/1/infinity QUEUE WITH BATCH ARRIVALS AND ONE QUEUE SKIPPING POLICY
- S. I. Matyushenko
- R. V. Razumchik
Abstract
Consideration is given to the discrete-time single-server system with one queue of infinite capacity and the geometric (Bernoulli) input flow. Customers are homogeneous, arrive in batches, and are served one by one in FIFO (first in, first out) manner. The sizes of arriving batches as well as the service times are assumed to be independent and identically distributed random variables with arbitrary discrete distributions. The queue skipping policy is implemented in the system: upon arrival of a batch, its size is compared with the current total number of customers in the system. If the size of the batch is larger than the system content, all customers residing in the system (including the one in server) are lost and the arrived batch enters the system; otherwise, the new batch leaves the system having no effect on it. Main stationary system performance characteristics, including those of the flow of lost customers, are obtained.
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[+] About this article
Title
STATIONARY CHARACTERISTICS OF DISCRETE-TIME Geo/G/1/infinity QUEUE WITH BATCH ARRIVALS AND ONE QUEUE SKIPPING POLICY
Journal
Informatics and Applications
2020, Volume 14, Issue 4, pp 25-32
Cover Date
2020-12-30
DOI
10.14357/19922264200404
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
discrete-time; queueing system; batch arrivals; queue skipping policy
Authors
S. I. Matyushenko  and R. V. Razumchik 
Author Affiliations
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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