ISSN:
1572-9443
Keywords:
G/M/s/r queue
;
batch arrivals
;
steady state existence
;
relations between arrival- and time-stationary probabilities
;
recursive stochastic equation
;
stationary point process
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract Consider aG/M/s/r queue, where the sequence{A n } n=−∞ ∞ of nonnegative interarrival times is stationary and ergodic, and the service timesS n are i.i.d. exponentially distributed. (SinceA n =0 is possible for somen, batch arrivals are included.) In caser 〈 ∞, a uniquely determined stationary process of the number of customers in the system is constructed. This extends corresponding results by Loynes [12] and Brandt [4] forr=∞ (withρ=ES0/EA0〈s) and Franken et al. [9], Borovkov [2] forr=0 ors=∞. Furthermore, we give a proof of the relation min(i, s)¯p(i)=ρp(i−1), 1⩽i⩽r + s, between the time- and arrival-stationary probabilities¯p(i) andp(i), respectively. This extends earlier results of Franken [7], Franken et al. [9].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01150044
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