On the infinite server shortest queue problem: Non-symmetric case

Authors:
Haishen Yao;Charles Knessl
Affiliations:
Department of Mathematics and Computer Science, Queensborough Community College, the City University of New York, Bayside 11364;Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, Chicago 60607-7045
Venue:
Queueing Systems: Theory and Applications
Year:
2006

Citing 3
Cited 0

Analysis of the asymmetric shortest queue problem

Queueing Systems: Theory and Applications
HEAVY TRAFFIC APPROXIMATIONS FOR A SYSTEM OF INFINITE SERVERS WITH LOAD BALANCING

Probability in the Engineering and Informational Sciences
A level-crossing approach to the solution of the shortest-queue problem

Operations Research Letters

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Abstract

We consider two parallel M/M/驴 queues. All servers in the first queue work at rate 驴1 and all in the second work at rate 驴2. A new arrival is routed to the system with the lesser number of customers. If both queues have equal occupancy, the arrival joins the first queue with probability 驴1, and the second with probability 驴2 = 1驴驴1. We analyze this model asymptotically. We assume that the arrival rate 驴 is large compared to the two service rates. We give several different asymptotic formulas, that apply for different ranges of the state space. The numerical accuracy of the asymptotic results is tested.