Journal of Applied Science and Engineering

Published by Tamkang University Press


Impact Factor




1Department of Mathematics, Damietta Faculty of Science, New Damietta, Egypt.


Received: November 23, 2000
Accepted: December 20, 2000
Publication Date: December 20, 2000

Download Citation: ||  


An alternative simple approach to Takâcs [8] procedure , which appears to economize in algebra is given. It is also shown that the measures of effectiveness such as the first and second order moments of the queue length can be easily obtained in a elegant closed form.

Keywords: Transient, Chebychev's polynomail, recurrence relations, Laplace transform


  1. [1] Abromowitz, M. and Stegun, I. A., Handbook of Mathematical Functions. New York, Dover, (1970).
  2. [2] Gross, D. and Harris, C. M., Fundamentals of Queuing Theory. John Wiley & Sons, New York, (1974).
  3. [3] Morse, P. M., Queues, Inventories and Maintenance. Wiley, New York, (1958)
  4. [4] Sharma, O. P., Markovian Queues. Ellis Horwood Ltd., England, (1990).
  5. [5] Sharma, O. P. and Dass, J., Multiserver Markovian queue with finite waiting space. Sankhya, Ser.B 50, pp. 428-431, (1989).
  6. [6] Sharma, O. P. and Gupta, U. C., Transient behaviour of an M/M/1/N queue, Stoch. Process and their Application, 13, pp. 327- 331, (1982).
  7. [7] Sharma, O. P. and Tarabia, A. M. K., A simple transient analysis of an M/M/1/N queue, Sankhya Ser. A, Vol. 62, Pt. 2, pp. 273-281, (2000).
  8. [8] Takâcs, L., Introduction to the theory of queues, Oxford University Press, (1960).
  9. [9] Tarabia, A. M. K., On the transient behaviour of a double-ended Markovian queue, Communicated, (2000).