eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-18
22:1
22:18
10.4230/LIPIcs.AofA.2018.22
article
Stationary Distribution Analysis of a Queueing Model with Local Choice
Dester, Plinio S.
1
Fricker, Christine
2
Mohamed, Hanene
3
INRIA Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
Département d’informatique de l’ENS, École normale supérieure, CNRS, PSL Research University, 75005 Paris, France, INRIA Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
Université Paris Nanterre, Modal'X, UPL, 92000 Nanterre, France
The paper deals with load balancing between one-server queues on a circle by a local choice policy. Each one-server queue has a Poissonian arrival of customers. When a customer arrives at a queue, he joins the least loaded queue between this queue and the next one, ties solved at random. Service times have exponential distribution. The system is stable if the arrival-to-service rate ratio called load is less than one. When the load tends to zero, we derive the first terms of the expansion in this parameter for the stationary probabilities that a queue has 0 to 3 customers. We investigate the error, comparing these expansion results to numerical values obtained by simulations. Then we provide the asymptotics, as the load tends to zero, for the stationary probabilities of the queue length, for a fixed number of queues. It quantifies the difference between policies with this local choice, no choice and the choice between two queues chosen at random.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol110-aofa2018/LIPIcs.AofA.2018.22/LIPIcs.AofA.2018.22.pdf
queueing model
local choice
stationary analysis
balance equations
power series expansion