On the queue-length distribution in the GIX/G/1 system with server vacations and exhaustive service

• Autorzy: Kempa W. M. W. M.
• Języki publikacji: EN

Abstrakty

EN

In the article the GIX /G/ 1 queueing system with server vacations and exhaustive service is investigated. For single and multiple vacations the queue-length transient distribution is studied first for a certain simplified system. Using the formula of total probability we direct the analysis to that for the system without vacations. The general case is obtained by applying the renewal theory approach. Explicit representations for Laplace transforms of queue-size distributions in systems with single and multiple vacations are obtained.

Słowa kluczowe

EN

queueing system with server vacations and exhaustive service; queue-length distribution

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2008
• Tom: Vol. 7, nr 2
• Strony: 23--30
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kempa W. M. W. M.

• Institute of Mathematics, Silesian University of Technology,

Bibliografia

• [1] Bratiychuk M.S., Kempa W.M., Application of the superposition of renewal processes to the study of batch arrival queues, Queueing Systems 2003, 44, 51-67.
• [2] Bratiychuk M.S., Kempa W.M., Explicite formulae for queue lenght of batch arrival systems, Stochastic Models 2004, 20(4), 457-472.
• [3] Kempa W.M., The virtual waiting time for the batch arrival queueing systems, Stochastic Analysis and Applications 2004, 22(5), 1235-1255.
• [4] Kempa W.M., The departure process for the queueing systems with batch arrival of customers, Stochastic Models 2008, 24(2), 246-263.
• [5] Baba Y., On the M X /G/1 queue with vacation time, Oper. Res. Lett. 1986, 5, 93-98.
• [6] Chatterjee U., Mukherjee S.P., On some distributions of the M X /G/1 queue with server’s vacation and exhaustive service discipline, Asis-Pac. J. Oper. Res. 1990, 7(1), 82-91.
• [7] Choudhury G., A bath arrival queue with a vacation time under single vacation policy, Comput. Oper. Res. 2002, 29(14), 1941-1955.
• [8] Choudhury G., Kalita S., Analysis of a bath arrival Poisson queue under single vacation policy, Calcutta Stat. Assoc. Bull. 2002, 53(209-210), 81-91.
• [9] Takagi H., Queueing Analysis, Volume 1: Vacation and Priority Systems, Part 1, North- Holland, Amsterdam-London-New York-Tokyo 1983.
• [10] Kempa W.M., Some new results for departure process in GI X /G/1queueing system with a single vacation time and exhaustive service, Stochastic Analysis and Applications (submitted in 2008).
• [11] Kempa W.M., GI /G/1/ batch arrival queueing system with a single exponential vacation, Mathematical Methods of Operations Research 2008 (accepted in 2007.