Open Problem—Load Balancing Using Delayed Information

Abstract

Load-balancing algorithms are important for efficiently routing jobs in systems of parallel queues; however, there has been relatively little attention devoted to developing algorithms in the presence of messaging and/or routing delays. Given a system of parallel queues with infinite capacity buffers; first-come, first-serve service discipline; and a single stream of incoming jobs that are routed by a dispatcher upon arrival, it has been shown that join the shortest queue (JSQ) satisfies certain optimality properties, including minimizing mean wait time when the job sizes are exponentially distributed ( Winston 1977 , Ephremides et al. 1980 ) and state space collapse of the queue lengths under heavy traffic scaling for general service distributions ( Reiman 1984 ). However, implementation of JSQ uses up-to-date information about the state of the buffers, which requires instantaneous exchange of multiple messages between the dispatcher and the queues. This challenge has led to the development of efficient algorithms that require fewer messages, including join the shortest of d queues (JSQ(d); Vvedenskaya et al. 1996 , Mitzenmacher 2001 ), join the idle queue (JIQ; Badonnel and Burgess 2008 , Lu et al. 2011 ), and persistent idle load distribution (PILD; Atar et al. 2019a , b ); see van der Boor et al. (2018) for a survey of some recent results in the many-server limit. Although these algorithms do not use full information about the system, they still use up-to-date information about the state of some of the queues. Because of the physical separation between the dispatcher and the queues, processing effects, or periodic updates from the queues, the dispatcher may have access only to information about the delayed states of the queues. (There may also be routing delays because of the time it takes a job to travel between the dispatcher and its assigned server, for which these algorithms also do not account.) In such settings, it has been shown that JSQ can perform quite poorly and lead to sustained oscillations in queue lengths ( Mitzenmacher 2000 ).