Using Inter-Arrival Times For Scheduling In Non-Observable Queues

Abstract

In online dispatching systems, when there is no opportunity to observe the state of the systems' components, one may implement "blind" scheduling policies i.e. those which use incomplete/indirect observations of the system state or do not use any information at all. Here we deal with the well-known problem of scheduling in several non-observable parallel single server queues with single Poisson incoming flow, when the broker (scheduler) does not observe neither the current states of the queues and servers, nor the size of the incoming jobs. The only available information is the job size distribution, server's speeds and job's inter-arrival time distribution. For this problem setting it is known that if the scheduler can memorize the sequence of its previous decisions, then a deterministic policy is much better than the probabilistic policy (with respect to the job's mean waiting and mean sojourn time). But if the broker can memorize its decision, it is also very natural to assume that it can also memorize the time instants at which these decisions are made. In this paper we address the following question: can the deterministic policy be improved if the broker, in addition to decisions made, utilizes also the information about the lengths of time between the decisions? We give numerical evidence that it is indeed possible; the cases presented include three, five and nine parallel •|M|1 queues. We describe the simple new policy according to which, the broker's decisions are based on the estimates of the queue sizes. In most of the numerical experiments, the new policy outperformed the deterministic policy The relative gain may reach 10% in the case of the job's mean sojourn time and 50% in the case of the job's mean waiting time. 1 I.e. the broker does not have a queue to store the jobs. 2 As, for example, demonstrated in Anselmi and Gaujal (2010).

Optimal Latency-Oriented Scheduling in Parallel Queuing Systems

“…The problem of scheduling Poisson arrivals from multiple sources on multiple queues, minimizing the response time for each source, can be solved using classical nonlinear optimization [8]. Policies can be found even if the state of the queues is not directly observable, getting a maximum likelihood estimate from the known capacity distributions [9] or employing periodic policies [10] that repeat actions in a predetermined sequence.…”