Results 1  10
of
27
Fluid Approximations And Stability Of Multiclass Queueing Networks: WorkConserving Disciplines
, 1995
"... This paper studies the fluid approximation (also known as the functional strong lawoflargenumbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the firstorder parameters (i. ..."
Abstract

Cited by 86 (9 self)
 Add to MetaCart
This paper studies the fluid approximation (also known as the functional strong lawoflargenumbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the firstorder parameters (i.e., longrun average arrivals, services and routings) of the queueing network. It is proved that the fluid approximation for the queueing network exists if the corresponding linear fluid model is weakly stable, and that the queueing network is stable if the corresponding linear fluid model is (strongly) stable. Sufficient conditions are found for the stabilities of a linear fluid model. Keywords and phrases: Multiclass queueing networks, fluid models, fluid approximations, stability, positive Harris recurrent, and workconserving service disciplines. Preliminary Versions: September 1993 Revisions: June 1994; September 1994; January 1995 To appear in Annals of Applied Probability AMS 1980 su...
Contact centers with a callback option and realtime delay information
 Operations Research
, 2004
"... doi 10.1287/opre.1030.0088 ..."
(Show Context)
Dynamic scheduling with convex delay costs: the generalized cµ rule
, 1995
"... We consider a general singleserver multiclass queueing system that incurs a delay cost Ck ( k) for each class k job that resides k units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a nite time horizon. ..."
Abstract

Cited by 52 (2 self)
 Add to MetaCart
(Show Context)
We consider a general singleserver multiclass queueing system that incurs a delay cost Ck ( k) for each class k job that resides k units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a nite time horizon. Denote the marginal delay cost and (instantaneous) service rate functions of class k by ck = C 0 k and k, and let ak(t) be the "age" or time that the oldest class k job has been waiting at time t. Wecall the scheduling policy that at time t serves the oldest waiting job of that class k with the highest index k(t)ck(ak(t)), the Generalized c Rule. As a dynamic priority rule that depends on very little data, the Generalized c Rule is attractive to implement. We show that with nondecreasing convex delay costs, the Generalized c Rule is asymptotically optimal if the system operates in heavy tra c, and give explicit expressions for the associated performance characteristics: the delay (throughput time) process and the minimum cumulative delay cost. The optimality result is robust in that it holds for a countable number of classes and several homogeneous servers in a nonstationary, deterministic or stochastic environment where arrival and service processes can be general and interdependent. 1
Learning and Value Function Approximation in Complex Decision Processes
, 1998
"... In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and sto ..."
Abstract

Cited by 41 (4 self)
 Add to MetaCart
In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and store a value function, which evaluates expected future reward as a function of current state. Unfortunately, exact computation of the value function typically requires time and storage that grow proportionately with the number of states, and consequently, the enormous state spaces that arise in practical applications render the algorithms intractable. In this thesis, we study tractable methods that approximate the value function. Our work builds on research in an area of artificial intelligence known as reinforcement learning. A point of focus of this thesis is temporaldifference learning  a stochastic algorithm inspired to some extent by phenomena observed in animal behavior. Given a selection of...
Positive Harris Recurrence and Diffusion Scale Analysis of a Push Pull Queueing Network
, 2009
"... We consider a push pull queueing network with two servers and two types of jobs which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is ..."
Abstract

Cited by 15 (11 self)
 Add to MetaCart
We consider a push pull queueing network with two servers and two types of jobs which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the KumarSeidman RybkoStolyar (KSRS) multiclass queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of jobs are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a reentrant line with infinite supply of work.
The Finite Element Method for Computing the Stationary Distribution of an SRBM in a Hypercube with Applications to Finite Buffer Queueing Networks
, 2002
"... This paper proposes an algorithm, referred to as BNA/FM (Brownian network analyzer with finite element method), for computing the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in a hypercube. The SRBM serves as an approximate model of queueing networks with finite buf ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
This paper proposes an algorithm, referred to as BNA/FM (Brownian network analyzer with finite element method), for computing the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in a hypercube. The SRBM serves as an approximate model of queueing networks with finite buffers. Our BNA/FM algorithm is based on finite element method and an extension of a generic algorithm developed by Dai and Harrison (1991). It uses piecewise polynomials to form an approximate subspace of an infinite dimensional functional space. The BNA/FM algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to BNA/SM (Brownian network analyzer with spectral method) of Dai and Harrison (1991), where global polynomials are used to form the approximate subspace and it sometime fails to produce meaningful estimates of these stationary probabilities. Extensive computational experiences from our implementation are reported that may be useful for future numerical research on SRBMs. A threestation tandem network with finite buffers are presented to illustrate the effectiveness of the Brownian approximation model and our BNA/FM algorithm.
Service system planning in the presence of a random arrival rate
, 2004
"... A fundamental workforce management challenge for inbound call center managers is to determine the number of agents to be scheduled to answer calls during each time period. These decisions are typically based on the desire to minimize cost while achieving some predetermined service objectives. These ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
A fundamental workforce management challenge for inbound call center managers is to determine the number of agents to be scheduled to answer calls during each time period. These decisions are typically based on the desire to minimize cost while achieving some predetermined service objectives. These service objectives are typically functionals of the customer queue time distributions, which in turn are highly dependent on the distribution of customer arrivals. The traditional call center modeling approach is to divide a given planning horizon into a series of time periods, and to assume a deterministic fixedrate Poisson arrival process for each period. These arrival processes then determine the performance measures that drive the selection of staffing levels. The arrival rate is very often not known with certainty, as we show in this paper through the analysis of historical data from several call centers. This type of uncertainty arises either because the arrival rate varies randomly over time or because the rate is simply unknown due to lack of information. In either case, the uncertainty in the arrival rate has major implications for the validity of traditional performance measures and consequently on the quality of staffing decisions. In this paper, we consider two potential forms of uncertainty in the arrival rates, and in each case address the question of what performance measures to use in order to support staffing decisions. We also explore ways to compute appropriate estimates for these performance measures. We clarify when the analytical approximations can be expected to be accurate and describe when and how simulation should be used to provide better estimates. 1
Steadystate analysis of reflected Brownian motions: characterization, numerical methods and queueing applications
, 1990
"... ..."
Diffusion Approximations for ReEntrant Lines with a FirstBufferFirstServed Priority Discipline
 Queueing Systems, Theory and Applications
"... The diffusion approximation is proved for a class of queueing networks, known as reentrant lines, under a firstbufferfirstserved (FBFS) service discipline. The diffusion limit for the workload process is a semimartingale reflecting Brownian motion on a nonnegative orthant. This approximation has ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
The diffusion approximation is proved for a class of queueing networks, known as reentrant lines, under a firstbufferfirstserved (FBFS) service discipline. The diffusion limit for the workload process is a semimartingale reflecting Brownian motion on a nonnegative orthant. This approximation has recently been used by Dai, Yeh and Zhou (1994) in estimating the performance measures of the reentrant lines with a FBFS discipline. Keywords: reentrant lines, diffusion approximation, multiclass queueing network, heavy traffic, semimartingale reflecting Brownian motion. AMS 1991 Subject Classifications: Primary 60F17, 60K25, 60G17; Secondary 60J70, 90B10, 90B22. First version: September 1995 Current version: May 1996 1 Supported in part by a grant from NSERC (Canada) . 2 Supported in part by a grant from NSERC (Canada); the research was done while the author was visiting the Faculty of Commerce and Business Administration, UBC, Canada. 1 Introduction We consider a class of multicl...