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Grier, Nathaniel; Massey, William A.; Mckoy, Tyrone; Whitt, Ward

doi:10.1023/a:1019176413237

Cited by 20 publications

(2 citation statements)

References 7 publications

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“…The envisaged application is a hospital emergency department, but the model can also be used in other applications. In [19], time-dependent arrival rates are called a key feature of many real life service systems and it is, therefore, included in the Erlang loss model which is presented. In [20], an overview of time-varying queueing models is presented, from a telecommunications point of view.…”

Section: Servers Arrivals Delay Resultsmentioning

confidence: 99%

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

2021

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In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

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Section: Servers Arrivals Delay Resultsmentioning

confidence: 99%

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

2021

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“…In some settings it may be important to consider them (Abdalla and Boucherie 2002;Aguir et al 2004;Hoffman and Harris 1986). Some of the many-server approximations apply there as well (e.g., Grier et al 1997;Mandelbaum, Massey, and Reiman 1998;Mandelbaum et al 1999;Massey 2002).…”

Section: Discussionmentioning

confidence: 99%

Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System

Green

Kolesar

Whitt

2007

Production and Operations Management

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236

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W e review queueing-theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long-run steady-state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time-dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time-lag refinements can improve traditional stationary independent period-by-period and peak-hour approximations. Time-varying infinite-server models help develop refinements, because closed-form expressions exist for their time-dependent behavior. More difficult cases with very long service times and other complicated features, such as end-of-day effects, can often be treated by a modified-offered-load approximation, which is based on an associated infinite-server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.

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The M / G / s / s Queue

Kharoufeh

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article describes the M / G / s / s queueing system, also known as the Erlang loss model . Customers arrive to this stochastic service system according to a homogeneous Poisson process and request service from one of s parallel servers ( s ≥ 1). The service times are assumed to be independent and identically distributed with a finite mean. Because there is no waiting space in the system, arriving customers who find all s servers busy are lost. Summarized herein are the primary operating characteristics of the M / G / s / s system, namely, the steady‐state probability distribution of the number of occupied servers and the steady‐state blocking probability (the Erlang B formula). Also summarized is the closely related delay probability (the Erlang C formula) for systems with unlimited waiting space. Some computational issues related to the Erlang B and C formulae are also discussed.

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Cited by 20 publications

References 7 publications

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System

The M / G / s / s Queue

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