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166
Telephone call centers: Tutorial, review, and research prospects
 Mgmt
, 2003
"... Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments trad ..."
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Cited by 295 (16 self)
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Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value – and at the same time fundamentally limited – in their ability to characterize system performance. We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research. Acknowledgments The authors thank Lee Schwarz, Wallace Hopp and the editorial board of M&SOM for initiating this project, as well as the referees for their valuable comments. Thanks are also due to L. Brown, A. Sakov, H. Shen, S. Zeltyn and L. Zhao for their approval of importing pieces of [36, 112].
Maximizing Queueing Network Utility Subject to Stability: Greedy Primaldual algorithm
 Queueing Systems
, 2005
"... We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision \produces " a certain vector of \commodities"; it also has assoc ..."
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Cited by 204 (9 self)
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We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision \produces " a certain vector of \commodities"; it also has associated \traditional " queueing control eect, i.e., it determines traÆc (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to nd a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable. We introduce a dynamic control algorithm, which we call Greedy PrimalDual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traÆc sources and network processing nodes may be randomly timevarying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traÆc rate constraints.
Crosslayer congestion control, routing and scheduling design in ad hoc wireless networks
 PROC. IEEE INFOCOM
, 2006
"... This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless ..."
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Cited by 151 (10 self)
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This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or singlerate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multirate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with timevarying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dualbased algorithm remains stable and optimal when the constraint set is modulated by an irreducible finitestate Markov chain. This paper thus presents a step toward a systematic way to carry out crosslayer design in the framework of “layering as optimization decomposition ” for timevarying channel models.
On the Asymptotic Optimality of the Gradient Scheduling Algorithm for MultiUser Throughput Allocation
 Operations Research
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Scheduling flexible servers with convex delay costs: Heavytraffic optimality of the generalized cμrule
 OPER. RES
, 2004
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Scheduling in a Queueing System with Asynchronously Varying Service Rates
 Probability in the Engineering and Informational Sciences
"... We consider the following queueing system which arises as a model of a wireless link shared by multiple users. There is a nite number N of input
ows served by a server. The system operates in discrete time t = 0; 1; 2; : : :. Each input
ow can be described as an irreducible countable Markov chain; ..."
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Cited by 94 (8 self)
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We consider the following queueing system which arises as a model of a wireless link shared by multiple users. There is a nite number N of input
ows served by a server. The system operates in discrete time t = 0; 1; 2; : : :. Each input
ow can be described as an irreducible countable Markov chain; waiting customers of each
ow are placed in a queue. The sequence of server states m(t); t = 0; 1; 2; : : : , is a Markov chain with nite number of states M. When server is in state m it can serve m i customers of ow i (in one time slot). The scheduling discipline is a rule that in each time slot chooses the
ow to serve based on the server state and the state of the queues. Our main result is that a simple online scheduling discipline, Modied Largest Weighted Delay First, along with its generalizations, is throughput optimal, namely it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region. 1
Maximum pressure policies in stochastic processing networks
, 2005
"... Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of s ..."
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Cited by 71 (6 self)
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Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of such systems. LPbased planning is critical in setting a medium range or longterm goal for many systems, but it does not translate into a daytoday operational policy that must deal with discreteness of jobs and the randomness of the processing environment. A stochastic processing network, advanced by J. Michael Harrison (2000, 2002, 2003), is a system that takes inputs of materials of various kinds and uses various processing resources to produce outputs of materials of various kinds. Such a network provides a powerful abstraction of a wide range of realworld systems. It provides highfidelity stochastic models in diverse economic sectors including manufacturing, service, and information technology. We propose a family of maximum pressure service policies for dynamically allocating service capacities in a stochastic processing network. Under a mild assumption on network structure, we prove that a network operating under a maximum pressure policy achieves maximum throughput predicted by LPs. These policies are semilocal in the sense that each
On Dynamic Scheduling of a Parallel Server System with Complete Resource Pooling
 In Analysis of Communication Networks: Call Centres, Traffic and Performance
, 2000
"... scientific noncommercial use only for individuals, with permission from the authors. We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several dif ..."
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Cited by 67 (5 self)
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scientific noncommercial use only for individuals, with permission from the authors. We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several different classes (or buffers). Jobs within a class are processed on a firstinfirstout basis, where the processing of a given job may be performed by any server from a given (classdependent) subset of the bank of servers. The random service time of a job may depend on both its class and the server providing the service. Each job departs the system after receiving service from one server. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs to available servers. We consider a parameter regime in which the system satisfies both a heavy traffic and a complete resource pooling condition. Our cost function is an expected cumulative discounted cost of holding jobs in the system, where the (undiscounted) cost per unit time is a linear function of normalized (with heavy traffic scaling) queue length. In a prior work [40], the second author proposed a continuous review threshold control policy for use in such a parallel server system. This policy was advanced as an “interpretation ” of the analytic solution to an associated Brownian control problem (formal heavy
Pathwise optimality of the exponential scheduling rule for wireless channels
 Advances in Applied Probability
, 2004
"... We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a s ..."
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Cited by 61 (19 self)
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We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called Exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {an},n = 1,2,...,N, we show that in a heavytraffic limit, under a nonrestrictive complete resource pooling condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes maxn an˜qn(t), where ˜qn(t) is user n queue length in the heavy traffic regime.
Optimal utility based multiuser throughput allocation subject to throughput constraints
 in Proc. IEEE INFOCOM
, 2005
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