Queues with Hyper-Poisson Input and Exponential Service Time Distribution with State Dependent Arrival and Service Rates

S. K. Gupta
Additional contact information
S. K. Gupta: Indian Institute of Technology, Kanpur, India

Operations Research, 1967, vol. 15, issue 5, 847-856

Abstract: The queuing system considered in this paper is characterized by (i) hyper-Poisson input with k branches with mean arrival rates depending upon the state of the system; (ii) first-come, first-served queue discipline; (iii) exponential service time distribution with mean service rate depending upon the state of the system; and (iv) finite waiting space. The functions defining the dependence of the mean arrival and service rates upon the state of the system are assumed to be arbitrary. Assuming steady-state conditions to obtain, a recurrence relation connecting the various probabilities introduced is found. By specifying a few particular forms of the state functions, graphs depicting two queue characteristics, viz., (i) probability of no delay, and (ii) mean number of units in the system are drawn. One of the particular cases has been interpreted as “a queuing problem with reneging” and another as “a multiple server queuing problem.”

Date: 1967
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.15.5.847 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:15:y:1967:i:5:p:847-856

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().