Decision Problems in Queueing Theory: a Numeric Application

Year 2024, Volume: 10 Issue: 2, 1 - 4, 31.12.2024

Erdinç Yücesoy

Abstract

The application of general behavioral patterns obtained from stochastic processes has always played an important role in Queuing Theory. Since the first studies in which optimization techniques were used in the decision-making process, design and control procedures have been included in studies especially in the field of statistics and operations. In the first studies where queuing systems were modeled and their operability was optimized, performance measures such as the block probability and the average waiting times in the system were considered in the decision-making process. With the availability of performance measures based on probabilistic methods in modeling queuing systems, the decision-making process has begun to be based on such measures. In this study probabilistic calculations of some performance measures of a custom queueing system is given in order to make a decision for optimum parameters of the system. In addition, a numerical example is given to illustrate the case.

Keywords

Queueing theory, stochastic process, decision process, optimization

References

• A. K. ERLANG. “Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges,” Elektroteknikeren,1917.
• F. POLLACZEK. “CONCERNING AN ANALYTICAL METHOD FOR THE treatment of queueing problems, in W. L. Smith and W. B. Wilkinson”, eds., Proceedings of the Symposium on Congestion Theory, University of North Carolina Press, Chapel Hill, NC, 1–42, 1965.
• N. T. J. BAILEY. “Study of queues and appointment systems in out-patient departments with special reference to waiting times”, J. Roy. Statist. Soc. B, 14, 185–199, 1952.
• W. LEDERMANN AND G. E. REUTER. “Spectral theory for the differential equations of simple birth and death processes”, Philos. Trans. Roy. Soc. London Ser. A, 246, 321–369, 1956.
• D. G. KENDALL. “Some problems in the theory of queues”, J. Roy. Statist. Soc. B, 13,151–185, 1956
• D. G. KENDALL,” Stochastic processes occurring in the theory of queues and their analysis by the method imbedded Markov chains”, Ann. Math. Statist., 24, 338–354, 1953
• S. STIDHAM, JR. “Editorial introduction, Queueing Systems”, 21 (special issue on optimal design and control of queueing systems), 239–243, 1995.
• T. B. CRABILL, D. GROSS, AND M. J. Magazine. “A classified bibliography of research on optimal design and control of queues”, Oper. Res., 25, 219–232, 1977.
• U. N. BHAT. “Parameter estimation in M/G/1 and GI/M/1 queues using queue length data, in S. K. Srinivasan and A. Vijayakumar”, eds., Stochastic Point Processes, Narosa, New Delhi, 96–107, 2003.