On Some Compound Random Variables Motivated by Bulk Queues
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-26
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We consider the distribution of the number of customers that arrive in an arbitrary bulk arrival queue system.
Under certain conditions on the distributions of the time of arrival of an arriving group ( Y ( t ) ) and its size ( X ) with respect to the considered bulk queue, we derive a general expression for the probability mass function of the random variable Q ( t ) which expresses the number of customers that arrive in this bulk queue during any considered period t .
Notice that Q ( t ) can be considered as a well-known compound random variable.
Using this expression, without the use of generating function, we establish the expressions for probability mass function for some compound distributions Q ( t ) concerning certain pairs ( Y ( t ) , X ) of discrete random variables which play an important role in application of batch arrival queues which have a wide range of applications in different forms of transportation.
In particular, we consider the cases when Y ( t ) and/or X are some of the following distributions: Poisson, shifted-Poisson, geometrical, or uniform random variable.
American Psychological Association (APA)
Meštrović, Romeo. 2015. On Some Compound Random Variables Motivated by Bulk Queues. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1073433
Modern Language Association (MLA)
Meštrović, Romeo. On Some Compound Random Variables Motivated by Bulk Queues. Mathematical Problems in Engineering No. 2015 (2015), pp.1-6.
https://search.emarefa.net/detail/BIM-1073433
American Medical Association (AMA)
Meštrović, Romeo. On Some Compound Random Variables Motivated by Bulk Queues. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1073433
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073433