SMS scnews item created by John Ormerod at Tue 7 Apr 2015 1407
Type: Seminar
Distribution: World
Expiry: 16 Apr 2015
Calendar1: 15 Apr 2015 1500-1600
CalLoc1: Carslaw 350
Auth: (jormerod) in SMS-WASM

Statistics Seminar: Moshe Haviv (Hebrew University of Jerusalem) -- The conditional distribution of the remaining service or vacation time in the single server queue with state dependent arrival rates


The somewhat overlooked queuing model of Mn/G/1 is like the well-known M/G/1 
(single server with a Poisson arrival process)  but with one key distinction: 
The Poisson arrival process has queue-length dependent rates. This model was 
dealt with by Yoav Kerner. In particular, a recursion for the distribution 
functions of the residual (remaining) service time given the number of the 
customers in the system was derived. In this paper we add the feature that 
the server takes (repeated) vacations whenever he becomes idle. The arrival 
rate vary both with the queue length and with the status of the server. We 
derive the corresponding recursions for this model. We note that the 
importance of having such results is in assessing the waiting time given how 
many are ahead upon arrival.

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