The multiclass GI/PH/N queue in the Halfin-Whitt regime

By Anatolii A. Puhalskii, Martin I. Reiman. Advances in Applied Probability, 2000

155 citations recorded by the source corpus.

Subfields: Management Information Systems, Management Science and Operations Research, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/6c486241927f8a6ca1aea3e53d8da66b305ca601

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Information Systems

1. Ward Whitt
2. Kavita Ramanan
3. Haya Kaspi
4. J. Dai
5. Tolga Tezcan
6. Shuangchi He
7. Josh E. Reed
8. Ger Koole

In Management Science and Operations Research

1. Kavita Ramanan
2. Haya Kaspi
3. Ward Whitt
4. Josh E. Reed
5. J. Dai
6. Tolga Tezcan
7. Shuangchi He
8. A. Mandelbaum

In Safety, Risk, Reliability and Quality

1. Ward Whitt
2. Haya Kaspi
3. A. Mandelbaum
4. Josh E. Reed
5. Ger Koole
6. J. Dai
7. Tolga Tezcan
8. Shuangchi He

Citations in the corpus

• Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System (2007, methodology): “Extensions to other many-server models have been developed by Puhalskii and Reiman (2000), Jelenkovic, Mandelbaum, and Moncilovic (2004), Zel-tyn and Mandelbaum (2005), and Whitt (2004a, 2005b).”
• SPDE Limits of Many Server Queues (2010, methodology): “We start by using results of [26] to recast the problem in a more convenient form.”
• Queueing Models of Call Centers: An Introduction (2002, methodology): “This was first discovered by Halfin and Whitt [28] for the M/M/s queue, and recently extended to M/PH/s in [43].”
• Telephone Call Centers: Tutorial, Review, and Research Prospects (2003, background): “Puhalskii and Reiman [128] prove weak convergence for (the queue and virtual wait) processes of the GI/PH/N system to a complex, multidimensional diffusion process, but not its steady state.”
• Steady-state analysis of a multiserver queue in the Halfin-Whitt regime (2007, background): “Phase-type service time distribution in the transient regime was considered in [35].”
• Proofs of the martingale FCLT (2007, methodology): “Specifically, this paper is intended to supplement Pang, Talreja and Whitt [17], which is an expository review paper illustrating how to do martingale proofs of many-server heavy-traffic limit theorems for Markovian queueing models, as in Krichagina and Puhalskii [10] and Puhalskii and Reiman [18].”
• The G/GI/N queue in the Halfin–Whitt regime (2009, background): “Puhalskii and Reiman [17] have demonstrated convergence of the G/PH/N queue length process in the Halfin and Whitt regime, where PH stands for phase type service time distributions.”
• On many-server queues in heavy traffic (2010, background): “This was first accomplished in the work of Halfin and Whitt [10] for the case of exponential service time distributions and has been continued by many additional authors as well for different classes of service time distributions, see, for instance, Jelenkovic, Mandelbaum, and Momcilovic [13], Mande”
• Dimensioning Large Call Centers (2000, unknown): “To this end, one could rst attempt the M/PH/N queue, following [14].”
• Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic (2004, methodology): “Further extensions were carried out by Puhalskii and Reiman [34] to cover a multiclass queue, phase-type service time distributions and priority scheduling policies, giving rise in the limit to a multidimensional diffusion process.”
• Many-server diffusion limits for G/Ph/n+GI queues (2010, methodology): “When the queues are critically loaded, our diffusion limit generalizes the result by Puhalskii and Reiman (2000) for GI/Ph/n queues without customer abandonment.”