Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

Ma, Ni; Whitt, Ward

doi:10.1016/j.spl.2015.11.018

Cited by 10 publications

(12 citation statements)

References 16 publications

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“…We used the composition construction for the arrival process in Section 2.1 to obtain the relatively simple one‐parameter characterization of its stochastic variability, which plays a key role in the supporting Theorems 2.1, 2.3, and 2.4, and in fitting the models to data, as discussed in Section 2.8. We also used the composition construction to efficiently generate the arrivals, exploiting , which employs table lookup from the inverse of the cumulative arrival rate function in (2.1). Conducting the simulation was challenging because

n = 10^{5}

replications were required to reliably estimate small blocking probabilities such as

B = 0.01

at each time point in a periodic cycle of length

100

.…”

Section: Resultsmentioning

confidence: 99%

“…Our use of the special composition construction in (2.3) follows , but this approach was proposed much earlier in and then again in . As emphasized in Remark 2.2 of , this construction is restrictive.…”

Section: Staffing In Time‐varying Many‐server Loss Modelsmentioning

confidence: 99%

“…

H_{2}

interarrival times. We then transformed time to convert this into a sinusoidal arrival rate, with our arrival rate function, using Algorithm 1 in . That algorithm exploits the inverse

Λ^{- 1}

of the cumulative arrival rate function

Λ

in (2.1).…”

Section: The Simulation Experimentsmentioning

confidence: 99%

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Many‐server loss models with non‐poisson time‐varying arrivals

Whitt

Zhao

2017

Naval Research Logistics

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This article proposes an approximation for the blocking probability in a many‐server loss model with a non‐Poisson time‐varying arrival process and flexible staffing (number of servers) and shows that it can be used to set staffing levels to stabilize the time‐varying blocking probability at a target level. Because the blocking probabilities necessarily change dramatically after each staffing change, we randomize the time of each staffing change about the planned time. We apply simulation to show that (i) the blocking probabilities cannot be stabilized without some form of randomization, (ii) the new staffing algorithm with randomiation can stabilize blocking probabilities at target levels and (iii) the required staffing can be quite different when the Poisson assumption is dropped. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 177–202, 2017

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n = 10^{5}

replications were required to reliably estimate small blocking probabilities such as

B = 0.01

at each time point in a periodic cycle of length

100

.…”

Section: Resultsmentioning

confidence: 99%

Section: Staffing In Time‐varying Many‐server Loss Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Many‐server loss models with non‐poisson time‐varying arrivals

Whitt

Zhao

2017

Naval Research Logistics

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“…(For additional details, see Ma and Whitt (2015).) To construct the vector b above and thus the function J in (6), we need two vectors of size n x and n y , where n x + n y = C(1 + ω)(1 + (1/λ U ))/ε.…”

Section: Generating the Arrival Processmentioning

confidence: 99%

Using simulation to study service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate

Ma¹,

Whitt²

2015

2015 Winter Simulation Conference (WSC)

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Simulation is used to evaluate the performance of alternative service-rate controls designed to stabilize performance in a queue with time-varying arrival rate, service in order of arrival and unlimited waiting space. Both Markovian and non-Markovian models are considered. Customer service requirements are specified separately from the service rate, which is subject to control. New versions of the inverse method exploiting tables constructed outside the simulation are developed to efficiently generate both the arrival times and service times. The simulation experiments show that a rate-matching service-rate control successfully stabilizes the expected queue length, but not the expected waiting time, while a new square-root servicerate control, based on a assuming that a pointwise-stationary approximation is appropriate, successfully stabilizes the expected waiting time when the arrival rate changes slowly compared to the expected service time.

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“…In this paper, therefore, we study the service rate controls that stabilize the mean virtual response time to a certain target value in a single server PS queue representing a computer server in a data center under time-varying arrival rates and controllable service rates, i.e., a GI t /GI t /1/P S queue. Our approach is similar to Whitt [1] and Ma and Whitt [6], who considered three different service rate controls, two of which were designed to stabilize the mean (virtual) waiting time in a GI t /GI t /1/F CF S queue. The slowly timevarying traffic patterns of internet services [5] justify our use of pointwise stationary approximation (PSA) [7].…”

Section: Introductionmentioning

confidence: 99%

Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates

Cho

2020

Ann Oper Res

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Motivated by the work of Whitt [1], who studied stabilization of the mean virtual waiting time (excluding service time) in a GI t /GI t /1/F CF S queue, this paper investigates the stabilization of the mean virtual response time in a single-server processor sharing (PS) queueing system with a time-varying arrival rate and a service rate control (a GI t /GI t /1/P S queue). We propose and compare a modified square-root (SR) control and a difference-matching (DM) control to stabilize the mean virtual response time of a GI t /GI t /1/P S queue. Extensive simulation studies with various settings of arrival processes and service times show that the DM control outperforms the SR control for heavy-traffic conditions, and that the SR control performs better for lighttraffic conditions.

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Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

Cited by 10 publications

References 16 publications

Many‐server loss models with non‐poisson time‐varying arrivals

Many‐server loss models with non‐poisson time‐varying arrivals

Using simulation to study service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate

Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates

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