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Asymptotically optimal staffing of service systems with joint QoS constraints
Springer Science and Business Media LLC - Tập 78 - Trang 359-386 - 2014
Jing Zan, John J. Hasenbein, David P. Morton
We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen–Van Leeuwaarden–Zwart bounds to obtain asy...... hiện toàn bộ
On the estimation of mixing coefficients for a multiphase service system
Springer Science and Business Media LLC - - 1997
Mark Kelbert, Alexandre Veretennikov
We consider a multiphase service system with a Poisson input flow. Its intensity depends on the number of customers under service. The stationary distribution for this system can be found in an explicit form. We study the rate of convergence to this stationary distribution as well as the bounds for some mixing coefficients. Coupling arguments and Liapunov's function approach form the basis of cons...... hiện toàn bộ
Sharp and simple bounds for the Erlang delay and loss formulae
Springer Science and Business Media LLC - Tập 64 - Trang 119-143 - 2009
Arie Harel
We prove some simple and sharp lower and upper bounds for the Erlang delay and loss formulae and for the number of servers that invert the Erlang delay and loss formulae. We also suggest simple and sharp approximations for the number of servers that invert the Erlang delay and loss formulae. We illustrate the importance of these bounds by using them to establish convexity proofs. We show that the ...... hiện toàn bộ
A new approach to the busy period of the M/M/1 queue
Springer Science and Business Media LLC - Tập 35 - Trang 105-115 - 2000
Kimberly K.J. Kinateder, Eui Yong Lee
In this paper, we provide a new approach to the computation of the Laplace transform of the length of the busy period of the M/M/1 queue with constrained workload (finite dam), without the use of complex analysis.
Appointments in care pathways: the $$Geo^x/D/1$$ queue with slot reservations
Springer Science and Business Media LLC - Tập 79 - Trang 37-51 - 2014
Maartje E. Zonderland, Richard J. Boucherie, Ahmad Al Hanbali
Motivated by the increasing popularity of care pathways in outpatient clinics, where some patients complete a significant part of the path in one day, hospitals aim to optimize the flow of these patients by prioritizing them in the appointment planning process. This paper considers the $$Geo^x/D/1$$ ...... hiện toàn bộ
Convergence in the total variation norm in multiserver queues
Springer Science and Business Media LLC - Tập 100 - Trang 293-295 - 2022
Sergey Foss
A new proof of finite moment conditions for GI/G/1 busy periods
Springer Science and Business Media LLC - Tập 4 - Trang 171-178 - 1989
Saeed Ghahramani, Ronald W. Wolff
A generalization of the GI/G/1 queue is considered where the service time of the nth customer and the inter-arrival time between arrivalsn andn+1 may be dependent random variables. New proofs are obtained of finite moment conditions for busy periods and the ladder epochs of a corresponding random walk. The method of proof, which is much different from the usual ones, directly relates busy period m...... hiện toàn bộ
Numerical approximations for the steady‐state waiting times in a GI/G/1 queue
Springer Science and Business Media LLC - Tập 31 - Trang 25-42 - 1999
B. Venkateshwara Rao, Richard M. Feldman
This paper focuses on easily computable numerical approximations for the distribution and moments of the steady‐state waiting times in a stable GI/G/1 queue. The approximation methodology is based on the theory of Fredholm integral equations and involves solving a linear system of equations. Numerical experimentation for various M/G/1 and GI/M/1 queues reveals that the methodology results in estim...... hiện toàn bộ
State space collapse for asymptotically critical multi-class fluid networks
Springer Science and Business Media LLC - Tập 59 - Trang 157-184 - 2008
Rosario Delgado
We consider a class of fluid queueing networks with multiple fluid classes and feedback allowed, which are fed by N heavy tailed ON/OFF sources. We study the asymptotic behavior when N→∞ of these queueing systems in a heavy traffic regime (that is, when they are asymptotically critical). As performance processes we consider the workload W N ...... hiện toàn bộ
Appointment-driven queueing systems with non-punctual customers
Springer Science and Business Media LLC - Tập 101 - Trang 1-56 - 2022
Oualid Jouini, Saif Benjaafar, Bingnan Lu, Siqiao Li, Benjamin Legros
We consider a single-server queueing system where a finite number of customers arrive over time to receive service. Arrivals are driven by appointments, with a scheduled appointment time associated with each customer. However, customers are not necessarily punctual and may arrive either earlier or later than their scheduled appointment times or may not show up at all. Arrival times relative to sch...... hiện toàn bộ
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