OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
c) Scheduling and dispatch of war material of special nature based on operational needs.
d) Scheduling of service facilities in a repair and maintenance workshop.
e) Scheduling of overhaul of used engines and other assemblies of aircrafts, missile systems, transport fleet
etc.
f) Scheduling of limited transport fleet to a large number of users.
g) Scheduling of landing and take off from airports with heavy duty of air traffic and air facilities.
h) Decision of replacement of plant, machinery, special maintenance tools and other equipment base on
different criteria.
Special benefits which this technique enjoys in solving problems such as above are
1) Queueing theory attempts to solve problems based on a scientific understanding of the problems
and solving them in optimal manner so that facilities are fully utilized and waiting time is reduced
to minimum possible.
2) Waiting time (or queueing) theory models can recommend arrival of customers to be serviced,
setting up of workstations, requirement of manpower etc. based on probability theory.
Limitations of Queueing Theory
Though queueing theory provides us a scientific method of understanding the queues and solving such problems, the
theory has certain limitations which must be understood while using the technique, some of these are:
a) Mathematical distribution, which are assume while solving queueing theory problems , are only a close
approximation of the behaviour of customers, time between their arrival and service time required by each
customer.
b) Most of real life queuing problems are complex situation and very difficult to use the queueing theory
technique, even then uncertainty will remain.
c) Many situations in industry and service are multi-channel queueing problems. When a customer has been
attended to and the service provided, it may still have to get some other service from another service and
may have to fall in queue once again. Here the departure of one channel queue becomes the arrival of other
queue. In such situations, the problem becomes still more difficult to analyse.
d) Queueing model may not be ideal method to solve certain very difficult and complex problems and one may
have to resort to other techniques like Monte-Carlo simulation method.
References
[1] Abou El-Ata M. O., Hariri A. M. A., “The M/M/C/N queue with balking and reneging” Computers and
Operations Research 19, pp. 713-716, 1992.
[2] Ancker Jr. C. J., Gafarian A. V., “Some queueing problems with balking and reneging”, I. Operations Research
11, pp. 88-100, 1963.
[3] Ancker Jr. C. J., Gafarian A. V., “Some queueing problems with balking and reneging”, II. Operations Research
11, pp. 928-937, 1963.
[4] Ancker Jr. C. J., Gafarian A. V., "Queueing with Impatient Customers who Leave at Random", J. Indust. Eng. 13,
pp. 86-87, 1962.
[5] Ancker Jr. C. J., Gafarian A. V., "Queueing with Reneging and Multiple Hetero-geneous servers”, Naval Res.
Log. Quart. 10, pp. 137-139, 1963.
[6]. Ancker Jr. C. J., Gafarian A. V., "Queuing with Reneging and Multiple Heterogeneous Servers", SP-372,
System Development Corporation, pp. 16-18, 1961.
[7] Avi-Itzhak B., Naor P., “Some queueing problems with the service station subject to breakdown”, Oper. Res., 11,
pp. 303-320, 1963.
[8] Barrer D.Y., “Queuing with impatient customers and ordered service”, Oper. Res. 5, pp. 650-656, 1957.
[9] Bbocmeyer E., Halstrom H. L., Jensen A., “The Life and Works of A. K. Erlang”, Copenhagen Telephone
Company, 1948.
[10] Boots N.K., Tijms H., “A multiserver queueing system with impatient customers”,Management Sci. 45, pp. 444-
448, 1999.
[11] Choi B.D., Kim B., Chung J., “M/M/1 queue with impatient customers of higher priority”, Queueing Systems
38, pp. 49-66. 2001.
[12] Crommelin C. D., “Delay Probability Formulae When the Holding Times Are Constant”, P. O. Elec. Eng. J. 25,
pp. 41-50, 1932.
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