Previous |  Up |  Next


The aim of the paper is to investigate queueing systems of the type $M/Mn$ (in equilibrium) in which customers to be served are selected from the queue: with fixed probabilities either the first customer or the last one is chosen. Using the standard method of generating functions the waiting time distribution and the outtaking probabilities are derived.
[1] F. Ferschl: Zufallsabhängige Wirtschaftsprozesse. Physica Veriag, Wien-Würzburg 1964. MR 0177801 | Zbl 0146.38701
[2] J. F. C. Kingman: The effect of queue discipline on waiting time variance. Proceed. Cambridge Phil. Soc., 58 (1962), 163-164. DOI 10.1017/S0305004100036331 | MR 0138137 | Zbl 0107.13101
[3] D. G. Tambouratzis: On a property of the variance of the waiting time of a queue. Journal of Applied Probability, 5 (1968), 702-703. DOI 10.2307/3211932 | MR 0246392 | Zbl 0179.47905
[4] O. Vašíček: Poznámka k čekací disciplíně v systémech hromadné obsluhy. Aplikace matematiky, 10 (1965), 423 - 427. MR 0205350
[5] F. Zítek: Über die Kundenreihenfolge in Bedienungssystemen. Aplikace matematiky, 15 (1970), 356-383. MR 0267667
[6] F. Zítek: Über die Kundenreihenfolge in Systemen $M/E_r/1$. Aplikace matematiky, 17 (1972), 191-208. MR 0297041
[7] F. Zítek: Sur l'ordre des clients dans les systèmes d'attente. Proceedings of the Fourth Conference on Probability Theory - Braşov, September 1971. Editura Academiei R. S. R., Bucureşti 1973, 607-619. MR 0405641
[8] F. Zítek: On a class of queue disciplines. Proceedings of the Fifth Conference on Probability Theory - Braşov, September 1974. (In print.)
Partner of
EuDML logo