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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
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......
On the estimation of mixing coefficients for a multiphase service system
Springer Science and Business Media LLC - - 1997
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......
Sharp and simple bounds for the Erlang delay and loss formulae
Springer Science and Business Media LLC - Tập 64 - Trang 119-143 - 2009
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 ......
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
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.
An M/G/1 queue with second optional service
Springer Science and Business Media LLC - Tập 34 - Trang 37-46 - 2000
We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate λ (>0) all demand the first ‘essential’ service, whereas only some of them demand the second ‘optional’ service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B(v) and that of the second optional service are exponential......
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
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
$$Geo^x/D/1$$
......
Convergence in the total variation norm in multiserver queues
Springer Science and Business Media LLC - Tập 100 - Trang 293-295 - 2022
Monotonicity and error bounds for networks of Erlang loss queues
Springer Science and Business Media LLC - Tập 62 - Trang 159-193 - 2009
Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are
Performance measures of interest such as loss probabilities or throughputs can b......
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
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......
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
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......
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