＜正＞This paper considers multiclass loss networks with monoskill and multiskill servers and overflow routing. Accordingly, an arriving job is assigned to a corresponding vacant monoskill server, if possible. Otherwi...
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＜正＞This paper considers multiclass loss networks with monoskill and multiskill servers and overflow routing. Accordingly, an arriving job is assigned to a corresponding vacant monoskill server, if possible. Otherwise the job is routed to a multiskill server, or rejected. We derive an efficiently computable upper bound for the system utilization by studying a modified routing where jobs can be redirected from multiskill to monoskill servers. This repacking policy improves performance also in terms of blocking probability when the service requirements of different job classes are statistically identical. Numerical simulations illustrate that our bounds provide good approximations for the performance of the original system.
Some open-loop and closed-loop control algorithms are discussed for an example of a discrete-event system, namely, the routing of arriving tasks from different arrival streams among several possible service stations. ...
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Some open-loop and closed-loop control algorithms are discussed for an example of a discrete-event system, namely, the routing of arriving tasks from different arrival streams among several possible service stations. It is shown that it is possible to design open-loop policies that give good performance in a way which is very robust with respect to large changes in the arrival rates. This is possible even though it is assumed that there is no online coordination between the routing algorithms for the different arrival streams. Some further improvements of the performance are possible when a simple feedback policy, namely, overflow routing, is implemented. This also gives reasonable robustness of performance with respect to changes in the service rates
This article studies multi-class loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer cl...
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This article studies multi-class loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by the packing of customers, altered service rates, and altered server configurations. This analysis leads to computationally fast upper and lower bounds for the performance of the system.
We consider multi-class blocking systems in which jobs require a single processing step. There are groups of servers that can each serve a different subset of all job classes. The assignment of jobs occurs according t...
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We consider multi-class blocking systems in which jobs require a single processing step. There are groups of servers that can each serve a different subset of all job classes. The assignment of jobs occurs according to some fixed overflow policy. We are interested in the blocking probabilities of each class. This model can be used for call centers, tele-communication and computer networks. An approximation method is presented that takes the burstiness of the overflow processes into account. This is achieved by assuming hyperexponential distributions of the inter-overflow times. The approximations are validated with simulation and we make a comparison to existing approximation methods. The overall blocking probability turns out to be approximated with high accuracy by several methods. However, the individual blocking probabilities per class are significantly more accurate for the method that is introduced in this paper. (C) 2005 Elsevier B.V. All rights reserved.
A multi-skill staffing problem in a call center where the agent skill sets are exogenous and the call routing policy has well-specified features of overflow between different agent types is addressed. Constraints are ...
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A multi-skill staffing problem in a call center where the agent skill sets are exogenous and the call routing policy has well-specified features of overflow between different agent types is addressed. Constraints are imposed on the service level for each call class, defined here as the steady-state fraction of calls served within a given time threshold, excluded. An approximation of these service levels is developed that allows an arbitrary overflow mechanism and customer abandonment. A two-stage heuristic that finds good solutions to mathematical programs with such constraints is developed. The first stage uses search methods supported by the approximation. Because service level approximation errors may be substantial, the solution is adjusted in a second stage in which performance is estimated by simulation. Realistic problems of varying size and routing policy are solved. The proposed approach is shown to be competitive with (and often better than) previously available methods. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix].
In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Once the arrival rate becomes known, the call center may be over-staffed, in which case staff are being paid to b...
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In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Once the arrival rate becomes known, the call center may be over-staffed, in which case staff are being paid to be idle, or under-staffed, in which case many callers hang-up in the face of long wait times. Firms that have chosen to keep their call center operations in-house can mitigate this problem by co-sourcing;that is, by sometimes outsourcing calls. Then, the required staffing N depends on how the firm chooses which calls to outsource in real time, after the arrival rate realizes and the call center operates as a M/M/N+M queue with an outsourcing option. Our objective is to find a joint policy for staffing and call outsourcing that minimizes the long-run average cost of this two-stage stochastic program when there is a linear staffing cost per unit time and linear costs associated with abandonments and outsourcing. We propose a policy that uses a square-root safety staffing rule, and outsources calls in accordance with a threshold rule that characterizes when the system is too crowded. Analytically, we establish that our proposed policy is asymptotically optimal, as the mean arrival rate becomes large, when the level of uncertainty in the arrival rate is of the same order as the inherent system fluctuations in the number of waiting customers for a known arrival rate. Through an extensive numerical study, we establish that our policy is extremely robust. In particular, our policy performs remarkably well over a wide range of parameters, and far beyond where it is proved to be asymptotically optimal.
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