On the Value Function of the M/G/1 FCFS and LCFS Queues

Hyytiä, Esa; Aalto, Samuli; Penttinen, Aleksi; Virtamo, Jorma

doi:10.1017/s0021900200012870

Cited by 6 publications

(6 citation statements)

References 30 publications

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“…When the processing times are known upon arrival, Harchol-Balter et al [15] proposed a routeing policy called the 'size interval task assignment with equal load (SITA-E)' where different servers are assigned to jobs with service times falling into particular intervals, and compared the performance of their policy with the performance of the JSW policy under different problem parameters. Hyytia et al [19] discussed the computation of value functions based on different levels of information for the routeing problem.…”

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confidence: 99%

Partial Flexibility in Routeing and Scheduling

Akgun

Righter

Wolff

2013

Advances in Applied Probability

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We consider partial customer flexibility in service systems under two different designs. In the first design, flexible customers have their own queue and each server has its own queue of dedicated customers. Under this model, the problem is a scheduling problem and we show under various settings that the dedicated customers first (DCF) policy is optimal. In the second design, flexible customers are not queued separately and must be routed to one of the server's dedicated queues upon arrival. We extend earlier results about the ‘join the smallest work (JSW)’ policy to systems with dedicated as well as flexible arrivals. We compare these models to a routeing model in which only the queue length is available in terms of both efficiency and fairness and argue that the overall best approach for call centers is JSW routeing. We also discuss how this can be implemented in call centers even when work is unknown.

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confidence: 99%

Partial Flexibility in Routeing and Scheduling

Akgun

Righter

Wolff

2013

Advances in Applied Probability

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“…This is slightly different than, e.g., in[20,22], where the holding costs are incurred also during the service time. In our case, an equivalent cost can be defined using service fees.…”

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confidence: 86%

Round-Robin Routing Policy: Value Functions and Mean Performance with Job- and Server-specific Costs

Hyytiä

Aalto

2014

Proceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools

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We study the Round-Robin (RR) routing to a system of parallel queues. The cost structure comprises two components: a service fee and a queueing delay related component, where both can be job-and queue-specific random variables. With Poisson arrivals, the inter-arrival time to each queue obeys Erlang's distribution. This allows us to study the mean and transient behavior of the queues separately. The service fee is independent of the queueing, and we obtain the corresponding mean cost rate and value function in closed forms. With respect to queueing delay, we first derive integral expressions enabling efficient computation of the corresponding value function. By decomposition, these yield also the value function for the whole system of m parallel queues fed by RR. Given the value function, one can carry out the first policy iteration step with arbitrary holding cost rates (e.g., delay, slowdown etc.) yielding efficient size-, cost-and state-aware policies. Moreover, the mean waiting time in an M/G/m-RR system gets resolved at the same time. The results are demonstrated in the numerical examples, where we compute near optimal task assignment policies for a sample system with two servers. KeywordsRound-Robin, M/G/m-RR, Erl/G/1 queue, Task assignment, Dispatching, Parallel queues, MDP

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“…Consequently, previous research has tended to focus on developing heuristic (sub-optimal) routing policies. For example, policies based on applying one step of policy iteration to a 'Bernoulli splitting' policy have been shown to perform strongly in various contexts (Krishnan 1990;Sassen et al 1997;Ansell et al 2003a;Bhulai and Koole 2003;Argon et al 2009;Hyytia et al 2012).…”

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confidence: 99%

A conservative index heuristic for routing problems with multiple heterogeneous service facilities

2020

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We consider a queueing system with N heterogeneous service facilities, in which admission and routing decisions are made when customers arrive and the objective is to maximize long-run average net rewards. For this type of problem, it is wellknown that structural properties of optimal policies are difficult to prove in general and dynamic programming methods are computationally infeasible unless N is small. In the absence of an optimal policy to refer to, the Whittle index heuristic (originating from the literature on multi-armed bandit problems) is one approach which might be used for decision-making. After establishing the required indexability property, we show that the Whittle heuristic possesses certain structural properties which do not extend to optimal policies, except in some special cases. We also present results from numerical experiments which demonstrate that, in addition to being consistently strong over all parameter sets, the Whittle heuristic tends to be more robust than other heuristics with respect to the number of service facilities and the amount of heterogeneity between the facilities.

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On the Value Function of the M/G/1 FCFS and LCFS Queues

Cited by 6 publications

References 30 publications

Partial Flexibility in Routeing and Scheduling

Partial Flexibility in Routeing and Scheduling

Round-Robin Routing Policy: Value Functions and Mean Performance with Job- and Server-specific Costs

A conservative index heuristic for routing problems with multiple heterogeneous service facilities

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