A heuristic rule for routing customers to parallel servers

Abstract

A practically important problem is the assignment of stochastically arriving service requests to one of several parallel service groups so as to minimize the long-run average sojourn time per service request. An exact solution of this multi-dimensional optimization problem is computationally infeasible.A simple heuristic solution method yielding a good suboptimal rule will be given for the case of server groups with different and generally distributed service times. This solution method is based on a decomposition approach and first principles from Markov decision theory. The main idea of the heuristic method is to apply one step of policy improvement to the best Bernoulli-splitting rule.

Dynamic Routing Policies for Multiskill Call Centers

“…Because the resulting policy will be too complicated to repeat the policy evaluation step, the algorithm stops here. In practice, for a suitably chosen approximation, the resulting policy is nearly optimal (see, e.g., Bhulai and Koole [2], Koole and Nain [13], Ott and Krishnan [17], and Sassen et al [20]). …”

“…The resulting improved policy is then used as an approximation for the optimal policy. This method has proven to be close to optimal in a variety of routing and assignment problems (see, e.g., Bhulai and Koole [2], Koole and Nain [13], Ott and Krishnan [17], and Sassen, Tijms, and Nobel [20]). …”

On the Control of a Queueing System with Aging State Information

“…This decoupling aspect has been used in, for instance, [15] where the authors derive state-dependent routing schemes for high-dimensional circuit-switched telephone networks, relying on the Bernoulli policy to allow an analysis of individual communication lines. Other applications include the control of traffic lights [8], inventory control [21], routing of telephone calls in call centers [5], and controlled queueing models [3,17].…”

Lookahead actions in dispatching to parallel queues

“…Given the so-called value function, one carries out the first policy iteration (FPI) step, which typically yields the greatest improvement towards the optimal policy. In the context of dispatching problems, this approach has been utilized to minimize the blocking probability, see Krishnan [15,16] and Leeuwaarden et al [17], and the sojourn time (i.e., delay or latency) or its generalization by arbitrary holding costs, see, e.g., Krishnan [18], Sassen et al [19], Bhulai et al [20] and Hyytiä et al [21][22][23]. Most dispatching systems considered have a rather complex state space (e.g., infinite number of waiting places, a continuous range of remaining service time, etc.)…”