Results 1  10
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21
Engineering solution of a basic callcenter model
 Management Science
, 2005
"... An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing modelM/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID custom ..."
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Cited by 45 (26 self)
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An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing modelM/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID customer abandonment times with a general distribution. Empirical studies indicate that the servicetime and abandontime distributions often are not nearly exponential, so that it is important to go beyond the MarkovianM/M/s/r+M special case, but the general servicetime and abandontime distributions make the realistic model very difficult to analyze directly. The proposed algorithm is based on an approximation by an appropriate Markovian M/M/s/r+M(n) queueing model, where M(n) denotes statedependent abandonment rates. After making an additional approximation, steadystate waitingtime distributions are characterized via their Laplace transforms. Then the approximate distributions are computed by numerically inverting the transforms. Simulation experiments show that the approximation is quite accurate. The overall algorithm can be applied to determine desired staffing levels, e.g., the minimum number of servers needed to guarantee that, first, the abandonment rate is below any specified target value and, second, that the conditional probability that an arriving customer will be served within a specified deadline, given that the customer eventually will be served, is at least a specified target value.
Approximation Techniques for Computing Packet Loss in FiniteBuffered Voice Multiplexers
 IEEE Journal on Selected Areas in Communications
, 1991
"... In this paper we examine three different approximation techniques for modeling packet loss in finitebuffer voice multiplexers. The performance models studied differ primarily in the manner in which the superposition of the voice sources (i.e., the arrival process) is modeled. The first approach ..."
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Cited by 39 (5 self)
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In this paper we examine three different approximation techniques for modeling packet loss in finitebuffer voice multiplexers. The performance models studied differ primarily in the manner in which the superposition of the voice sources (i.e., the arrival process) is modeled. The first approach models the superimposed voice sources as a renewal process and performance calculations are based only on the first two moments of the renewal process. The second approach is based on modeling the superimposed voice sources as a Markov Modulated Poisson Process (MMPP). Our choice of parameters for the MMPP attempts to capture aspects of the arrival process in an alternate, more intuitive, manner than previously proposed approaches for determining the MMPP parameters and is shown to compute loss more accurately. Finally, we also evaluate a fluid flow approximation for computing packet loss. For all three approaches, we consider as a unifying example, the case of multiplexing voice sou...
Optimizing call center staffing using simulation and analytic center cutting plane methods
 Management Science
, 2005
"... We consider the problem of minimizing staffing costs in an inbound call center, while maintaining an acceptable level of service in multiple time periods. The problem is complicated by the fact that staffing level in one time period can affect the service levels in subsequent periods. Moreover, sta ..."
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Cited by 28 (0 self)
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We consider the problem of minimizing staffing costs in an inbound call center, while maintaining an acceptable level of service in multiple time periods. The problem is complicated by the fact that staffing level in one time period can affect the service levels in subsequent periods. Moreover, staff schedules typically take the form of shifts covering several periods. Interactions between staffing levels in different time periods, as well as the impact of shift requirements on the staffing levels and cost should be considered in the planning. Traditional staffing methods based on stationary queueing formulas do not take this into account. We present a simulationbased analytic center cutting plane method to solve a sample average approximation of the problem. We establish convergence of the method when the service level functions are discrete pseudoconcave. An extensive numerical study of a moderately large call center shows that the method is robust and, in most of the test cases, outperforms traditional staffing heuristics that are based on analytical queueing methods.
Realtime delay estimation based on delay history
, 2007
"... Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the ..."
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Cited by 14 (4 self)
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Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delayhistory estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multiserver queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the manyserver and classical heavytraffic limiting regimes.
Managing the overflow of intensive care patients
 European Journal of Operational Research
, 2008
"... Abstract. Many hospitals in the Netherlands are confronted with capacity problems at their Intensive Care Units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because juridicall ..."
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Cited by 9 (0 self)
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Abstract. Many hospitals in the Netherlands are confronted with capacity problems at their Intensive Care Units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because juridically, as well as for hospital logistics, rejecting emergency patients has minimal consequences for the hospital. As a result, emergency patients occasionally have to be transported to hospitals far away. In this work, we propose a cooperative solution for the ICU capacity problem. In our model, several hospitals in a region jointly reserve a small number of beds for regional emergency patients. We present a mathematical method for computing the number of regional beds for any given acceptance rate. The analytic approach is inspired by overflow models in telecommunication systems with multiple streams of telephone calls. Simulation studies show that our model is quite accurate. We conclude that cooperation between hospitals helps to achieve a high acceptance level with a smaller number of beds resulting in improved service for all patients. 1.
Representing workloads in GI/G/1 queues through the preemptiveresume LIFO queue discipline, " Queueing Sys
 Theory and Appl
, 1988
"... We give in this paper a detailed sampleaverage analysis of GI/G/1 queues with the preemptiveresume LIFO (lastinfirstout) queue discipline: We study the longrun “state” behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express ..."
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Cited by 8 (4 self)
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We give in this paper a detailed sampleaverage analysis of GI/G/1 queues with the preemptiveresume LIFO (lastinfirstout) queue discipline: We study the longrun “state” behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptiveresume LIFO queue discipline is workconserving, imply new representations for both “actual ” and “virtual ” delays in standard GI/G/1 queues with the FIFO (firstinfirstout) queue discipline. The arguments by which our results are obtained unveil the underlying structural “explanations ” for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the wellknown Beneˇs’s formula for the delay distribution in M/G/1. We also discuss how to extend our results to settings more general than GI/G/1.
Duality and Other Results for M/G/1 and GI/M/1 Queues, via a New Ballot Theorem
 Mathematics of Operations Research
, 1989
"... We generalize the classical ballot theorem and use it to obtain direct probabilistic derivations of some wellknown and some new results relating to busy and idle periods and waiting times in M/G/1 and GI/M/1 queues. In particular, we uncover a duality relation between the joint distribution of seve ..."
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Cited by 6 (4 self)
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We generalize the classical ballot theorem and use it to obtain direct probabilistic derivations of some wellknown and some new results relating to busy and idle periods and waiting times in M/G/1 and GI/M/1 queues. In particular, we uncover a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 and the corresponding joint distribution in GI/M/1. In contrast with the classical derivations of queueing theory, our arguments avoid the use of transforms, and thereby provide insight and termbyterm “explanations ” for the remarkable forms of some of these results.
Relating polling models with zero and nonzero switchover times
 Queueing Systems
, 1995
"... We consider a system of N queues served by a single server in cyclic order. Each queue has its own distinct Poisson arrival stream and its own distinct general servicetime distribution (asymmetric queues); and each queue has its own distinct distribution of switchover time (the time required for th ..."
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Cited by 5 (2 self)
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We consider a system of N queues served by a single server in cyclic order. Each queue has its own distinct Poisson arrival stream and its own distinct general servicetime distribution (asymmetric queues); and each queue has its own distinct distribution of switchover time (the time required for the server to travel from that queue to the next). We consider two versions of this classical polling model: In the first, which we refer to as the zeroswitchovertimes model, it is assumed that all switchover times are zero and the server stops traveling whenever the system becomes empty. In the second, which we refer to as the nonzeroswitchovertimes model, it is assumed that the sum of all switchover times in a cycle is nonzero and the server does not stop traveling when the system is empty. After providing a new analysis for the zeroswitchovertimes model, we obtain, for a host of service disciplines, transform results that completely characterize the relationship between the waiting times in these two, operationallydifferent, polling models. These results can be used to derive simple relations that express (all) waitingtime moments in the nonzeroswitchovertimes model in terms of those in the zeroswitchovertimes model. Our results, therefore, generalize corresponding results for the expected waiting times obtained recently by Fuhrmann [8] and Cooper, Niu, and Srinivasan [4]. Key words. Polling models, cyclic queues, waiting times, decomposition, switchover times, vacation models. 1
TransformFree Analysis of M/G/1/K and Related Queues
 Math of Oper Res
, 1993
"... Using constructive, samplepath arguments, we derive a variety of transformfree results about queue lengths and waiting times for the M/G/1/K queue. In classical analyses of M/G/1/K, it is typical to work with Markov processes obtained by defining the “state ” of the system at a time epoch to be th ..."
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Cited by 3 (1 self)
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Using constructive, samplepath arguments, we derive a variety of transformfree results about queue lengths and waiting times for the M/G/1/K queue. In classical analyses of M/G/1/K, it is typical to work with Markov processes obtained by defining the “state ” of the system at a time epoch to be the number of customers present and, as supplementary information, the remaining service time of the customer, if any, in service. In contrast, the key idea behind our analysis is to work with a modified Markov process that has a moredetailed state description: At any time epoch t when the server is busy, we replace “the number of customers present ” by two variables, namely (a) the number of customers who were (and still are) waiting in the queue immediately after the start of the service in progress, and (b) the number of customers who arrived during that same service but prior to t. We show that this minor change of state definition, coupled with a rigorous formalization of the intuitive notion of a “test customer ” (whose viewpoint is adopted in our analysis of the modified Markov process), makes possible a surprisingly simple analysis of the M/G/1/K queue. We also show that our method can be extended easily to yield similar results for several generalizations of the basic M/G/1/K model.
REALTIME DELAY ESTIMATION IN CALL CENTERS
"... We use computer simulation to study the performance of alternative realtime delay estimators in heavily loaded multiserver queueing models. These delay estimates may be used to make delay announcements in call centers and related service systems. We consider the classical delay estimator based on t ..."
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We use computer simulation to study the performance of alternative realtime delay estimators in heavily loaded multiserver queueing models. These delay estimates may be used to make delay announcements in call centers and related service systems. We consider the classical delay estimator based on the queue length, QLs, which multiplies the queue length plus one times the mean interval between successive service completions, ignoring customer abandonment. We show that QLs has a superior performance in the GI/M/s model, but that there is a need to go beyond it in the GI/GI/s + GI model, allowing abandonment. To this end, we propose new, simple and effective, delay estimators based on the queue length. We also consider a delay estimator based on recent customer delay history in the system: the delay of the last customer to enter service, LES. 1