DocumentCode :
747602
Title :
Waiting time distribution for the M/M/m queue
Author :
Chan, W.-C. ; Lin, Y.-B.
Author_Institution :
Inst. of Comput. Sci. & Inf. Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan
Volume :
150
Issue :
3
fYear :
2003
fDate :
6/1/2003 12:00:00 AM
Firstpage :
159
Lastpage :
162
Abstract :
A novel method is presented for the calculation of the waiting time distribution function for the M/M/m queue. It is shown that the conditional waiting time obeys an Erlang distribution with rate mμ, where μ is the service rate of a server. An explicit closed form solution is obtained by means of the probability density function of the Erlang distribution. The derivation of the result proved to be very simple. The significance of Khintchine´s (1969) method and its close relation to the proposed method is pointed out. It is also shown that the waiting time distribution can be obtained from Takacs´s (1961) waiting time distribution for the G/M/m queue as a special case. This reveals some insight into the significance of Takacs´s more general, but rather complex, result.
Keywords :
probability; queueing theory; Erlang distribution; Khintchine´s method; M/M/m queue; conditional waiting time; explicit closed form solution; probability density function; service rate; waiting time distribution;
fLanguage :
English
Journal_Title :
Communications, IEE Proceedings-
Publisher :
iet
ISSN :
1350-2425
Type :
jour
DOI :
10.1049/ip-com:20030274
Filename :
1214605
Link To Document :
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