The Annals of Applied Probability

Randomized scheduling algorithm for queueing networks

Devavrat Shah and Jinwoo Shin

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There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling algorithms for constrained queueing network models that arise in the context of emerging communication networks. Here we consider two representative models. One, a queueing network model that captures randomly varying number of packets in the queues present at a collection of wireless nodes communicating through a shared medium. Two, a buffered circuit switched network model for an optical core of future internet to capture the randomness in calls or flows present in the network. The maximum weight scheduling algorithm proposed by Tassiulas and Ephremides [IEEE Trans. Automat. Control 37 (1992) 1936–1948], leads to a myopic and stable algorithm for the packet-level wireless network model. But computationally it is expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of nonpreemption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

Article information

Ann. Appl. Probab. Volume 22, Number 1 (2012), 128-171.

First available in Project Euclid: 7 February 2012

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Zentralblatt MATH identifier

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 68M12: Network protocols
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Wireless medium access buffered circuit switched network aloha stability scheduling mixing time slowly varying Markov chain


Shah, Devavrat; Shin, Jinwoo. Randomized scheduling algorithm for queueing networks. Ann. Appl. Probab. 22 (2012), no. 1, 128--171. doi:10.1214/11-AAP763.

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