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Scheduling flexible servers with convex delay costs in manyserver service systems. Manufacturing Service Oper. Management forthcoming
 Costs in ManyServer Service Systems. Manufacturing and Service Operations Management. Forthcoming
, 2007
"... In a recent paper we introduced the queueandidlenessratio (QIR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to se ..."
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Cited by 20 (15 self)
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In a recent paper we introduced the queueandidlenessratio (QIR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, QIR produces an important statespace collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That statespace collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of QIR stochastically minimizes convex holding costs in a finitehorizon setting when the service rates are restricted to be pooldependent. Under additional regularity conditions, the special version of QIR reduces to a simple policy: Linear costs produce a prioritytype rule, in which the leastcost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a manyserver analogue of the generalizedcµ (Gcµ) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.
Blind fair routing in largescale service systems
, 2011
"... In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skil ..."
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Cited by 7 (0 self)
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In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skill levels. A further complication is that it is preferable that these decisions are made blindly; that is, they depend only on the system state and not on system parameter information such as call arrival rates and service speeds. This is because this information is generally not known with certainty. Ideally, a dynamic control policy for making routing and scheduling decisions balances customer and server needs, by keeping customer delays low, but still fairly dividing the workload amongst the various servers. In this paper, we propose two blind dynamic control policies for parallel server systems with multiple customer classes and server pools, one that is based on the number of customers waiting and the number of agents idling, and one that is based on customer delay times and server idling times. We show that, in the HalfinWhitt manyserver heavy traffic limiting regime, our proposed blind policies perform extremely well when the objective is to minimize customer holding or delay costs subject to “server fairness”, as defined by how the system idleness is divided among servers. To do this, we formulate an approximating diffusion control problem (DCP), and compare the performance of the nonblind DCP solution to a feasible policy for the DCP that is blind. We establish that the increase in the DCP objective function value is small over a wide range of parameter values. We then use simulation to validate that a small increase in the DCP objective function value is indicative of our proposed blind policies performing very well. Acknowledgement: We thank Itay Gurvich and Avi Mandelbaum for many valuable discussions.
Marginal Bidding: An Application of the Equimarginal Principle to Bidding in TAC SCM
"... Abstract. We present a fast and effective bidding strategy for the Trading Agent Competition in Supply Chain Management (TAC SCM). In TAC SCM, manufacturers compete to procure computer parts from suppliers (the procurement problem), and then sell assembled computers to customers in reverse auctions ..."
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Cited by 2 (1 self)
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Abstract. We present a fast and effective bidding strategy for the Trading Agent Competition in Supply Chain Management (TAC SCM). In TAC SCM, manufacturers compete to procure computer parts from suppliers (the procurement problem), and then sell assembled computers to customers in reverse auctions (the bidding problem). This paper is concerned only with bidding, in which an agent must decide how many computers to sell and at what prices to sell them. We propose a greedy solution, Marginal Bidding, inspired by the Equimarginal Principle, which states that revenue is maximized among possible uses of a resource when the return on the last unit of the resource is the same across all areas of use. We show experimentally that certain variations of Marginal Bidding can compute bids faster than our ILP solution, which enables Marginal Bidders to consider future demand as well as current demand, and hence achieve greater revenues when knowledge of the future is valuable. 1
Convergent Lagrangian heuristics for nonlinear minimum cost network flows
, 2007
"... We consider the separable nonlinear and strictly convex singlecommodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain ..."
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We consider the separable nonlinear and strictly convex singlecommodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not available from a Lagrangian dual vector unless it is optimal. The scheme is constructed such that if we apply it from a sequence of Lagrangian dual vectors that converge to an optimal one, then the resulting primal (feasible) vectors converge to the unique optimal primal flow vector. It is therefore also a convergent Lagrangian heuristic, akin to those primarily devised within the field of combinatorial optimization but with the contrasting and striking advantage that it is guaranteed to yield a primal optimal solution in the limit. Thereby we also gain access to a new stopping criterion for any Lagrangian dual algorithm for the problem, which is of interest in particular if the SSCNFP arises as a subproblem in a more complex model. We construct instances of convergent Lagrangian heuristics that are based on graph searches within the residual graph, and therefore are efficiently implementable; in particular we consider two shortest path based heuristics that are based on the optimality conditions of the original problem. Numerical experiments report on the relative efficiency and accuracy of the various schemes. 1
A Library for Continuous Convex Separable Quadratic Knapsack Problems
"... The Continuous Convex Separable Quadratic Knapsack problem (CQKnP) is an easy but useful model that has very many different applications. Although the problem can be solved quickly, it must typically be solved very many times within approaches to (much) more difficult models; hence an efficient solu ..."
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The Continuous Convex Separable Quadratic Knapsack problem (CQKnP) is an easy but useful model that has very many different applications. Although the problem can be solved quickly, it must typically be solved very many times within approaches to (much) more difficult models; hence an efficient solution approach is required. We present and discuss a small opensource library for its solution that we have recently developed and distributed.
Acknowledgement
, 2007
"... In a recent paper we introduced the fixedqueueratio (FQR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) wh ..."
Abstract
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In a recent paper we introduced the fixedqueueratio (FQR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, FQR produces an important statespace collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That statespace collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of FQR stochastically minimizes convex holding costs in a finitehorizon setting when the service rates are restricted to be pooldependent. Under additional regularity conditions, the special version of FQR reduces to a simple policy: Linear costs produce a prioritytype rule, in which the leastcost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a manyserver analogue of the generalizedcµ (Gcµ) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.