 Some Queuing Problems with Balking and Reneging. IC. J. Ancker and
A. V. Gafarian
Operations Research, 1963, vol. 11, issue 1, 88-100 Abstract: Balking (refusing to join the queue) and reneging (leaving the queue after entering) are considered. The model assumes (1) Customers arrive from a single infinite source in a Poisson stream (2) Arriving customers balk with probability n / N where n is the number in system and N is the maximum number allowed in the system (3) Joining customers renege if service does not begin by a certain time, which is a random variable with negative exponential distribution (4) A single-service facility operates on a first-come, first-served basis with negative exponential service time distribution. For the steady state, the following are obtained the state probabilities, mean number in queue and system, the probability of R or more in system, the probabilities of balking, waiting, reneging, and acquiring service, the customer loss rate, the distribution and mean value of time in queue for customers who acquire service, and the corresponding results for those who renege. All of these results are also obtained for a pure balking system (no reneging) by setting the reneging parameter equal to zero. This case may be interpreted as the simple machine interference problem for which some of our results appear to be new. Date: 1963 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:11:y:1963:i:1:p:88-100 Access Statistics for this article More articles in Operations Research from INFORMS Contact information at EDIRC. |
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