Results 11  20
of
52
Optimal Control of Parallel Server Systems with Many Servers in Heavy Traffic
, 2008
"... We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the manyserver heavy traffic regi ..."
Abstract

Cited by 16 (7 self)
 Add to MetaCart
We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the manyserver heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponentially distributed.
Control of systems with flexible multiserver pools: a shadow routing approach
 QUEUEING SYST (2010 ) 66 : 1–51
, 2010
"... A general model with multiple input flows (classes) and several flexible multiserver pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization pr ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
A general model with multiple input flows (classes) and several flexible multiserver pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within O(√r)of its capacity. The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least O ( √ r) average queue lengths, even if the so called nullcontrollability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006) on a finite time interval is possible; strategies achieving this O(√r) growth rate we call orderoptimal. (ii) We show that some natural algorithms, such as MaxWeight, that guarantee stability, are not orderoptimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to orderoptimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme.
CrossSelling in a Call Center with a Heterogeneous Customer Population
, 2006
"... This is the technical appendix accompanying the paper, “CrossSelling in a Call Center with a Heterogeneous Customer Population, ” [3]. The organization of this appendix is as follows: we begin in §B with the completion of the proof of Proposition 1, whose sketch was given in §A of [3]. We continue ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
This is the technical appendix accompanying the paper, “CrossSelling in a Call Center with a Heterogeneous Customer Population, ” [3]. The organization of this appendix is as follows: we begin in §B with the completion of the proof of Proposition 1, whose sketch was given in §A of [3]. We continue in §C with some preliminaries required for the performance analysis of (S)(C).
Central limit theorem for a manyserver queue with random service rates
 Ann. Appl. Probab
, 2008
"... Given a random variable N with values in N, and N i.i.d. positive random variables {µk}, we consider a queue with renewal arrivals and N exponential servers, where server k serves at rate µk, under two work conserving routing schemes. In the first, the service rates {µk} need not be known to the rou ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
Given a random variable N with values in N, and N i.i.d. positive random variables {µk}, we consider a queue with renewal arrivals and N exponential servers, where server k serves at rate µk, under two work conserving routing schemes. In the first, the service rates {µk} need not be known to the router, and each customer to arrive at a time when some servers are idle is routed to the server that has been idle for the longest time (or otherwise it is queued). In the second, the service rates are known to the router, and a customer that arrives to find idle servers is routed to the one whose service rate is greatest. In the manyserver heavy traffic regime of Halfin and Whitt, the process that represents the number of customers in the system is shown to converge to a onedimensional diffusion with a random drift coefficient, where the law of the drift depends on the routing scheme. A related result is also provided for nonrandom environments. 1. Introduction. Manyserver
Servicelevel differentiation in call centers with fully flexible servers
 Management Sci
"... doi 10.1287/mnsc.1070.0825 ..."
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 ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
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.
Staffing Call Centers with Uncertain Demand Forecasts: A ChanceConstrained Optimization Approach
, 2010
"... We consider the problem of staffing call centers with multiple customer classes and agent types operating under qualityofservice (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability wi ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We consider the problem of staffing call centers with multiple customer classes and agent types operating under qualityofservice (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chanceconstrained formulation with the averageperformance constraints that have been used so far in the literature. We then propose a twostep solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a firstorder (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates—the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.
Routing and staffing in largescale service systems: The case of homogeneous impatient customers and heterogeneous servers
, 2011
"... ..."
(Show Context)
Queueing Systems with Heterogeneous Servers: Improving Patients
 Flow in Hospitals. Technion M.Sc. Research Proposal
, 2007
"... During the last century and the beginning of the present one, the service sector has grown significantly and now accounts for approximately 70 % of the national income in the United States, and similarly in many other Western countries. The service sector covers a wide spectrum of activities, e.g. e ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
During the last century and the beginning of the present one, the service sector has grown significantly and now accounts for approximately 70 % of the national income in the United States, and similarly in many other Western countries. The service sector covers a wide spectrum of activities, e.g. education, professional services, financial services and
When promotions meet operations: Crossselling and its effect on callcenter performance
, 2006
"... We study crossselling operations in call centers. The following question is addressed: How many customer service representatives are required (staffing) and when should crossselling opportunities be exercised (control) in a way that will maximize the expected profit of the firm while maintaining a ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
We study crossselling operations in call centers. The following question is addressed: How many customer service representatives are required (staffing) and when should crossselling opportunities be exercised (control) in a way that will maximize the expected profit of the firm while maintaining a prespecified service level target. We tackle these questions by characterizing scheduling and staffing schemes that are asymptotically optimal in the limit, as the system load grows to infinity. Our main finding is that a threshold priority (TP) control, in which crossselling is exercised only if the number of callers in the system is below a certain threshold, is asymptotically optimal in great generality. The asymptotic optimality of TP reduces the staffing problem to the solution of a simple deterministic problem, in some cases, and to a simple search procedure in others. Our asymptotic approach establishes that our staffing and control scheme is nearoptimal for large systems. In addition, we numerically demonstrate that TP performs extremely well even for relatively small systems.