Title :
A MAP/SM/1 queue with service times depending on the arrival process
Author :
Machihara, Fumiaki
Author_Institution :
Dept. of Inf. Sci., Tokyo Denki Univ., Saitama, Japan
Abstract :
We study a MAN/SM/1 queue with Markov arrival process input and semi-Markov service. Service times may depend on the arrival phase states, that is, there are many types of arrivals which have different service time distributions. At first, we derive the joint distribution of the numbers of different types of customers at departures. The distributions of the virtual and actual waiting times as well as the queue length distributions at an arbitrary time, arrivals, and departures are derived
Keywords :
Markov processes; probability; queueing theory; MAP/SM/1 queue; Markov arrival process; Markov renewal process; arrival phase states; arrival process; joint distribution; probability; queue length distributions; semiMarkov service; service times; Convolution; Customer service; Equations; Hip; Queueing analysis; Samarium; Stationary state; Stochastic processes; Tin;
Conference_Titel :
Systems, Man, and Cybernetics, 1996., IEEE International Conference on
Conference_Location :
Beijing
Print_ISBN :
0-7803-3280-6
DOI :
10.1109/ICSMC.1996.561474
