$$G/{ GI}/N(+{ GI})$$ queues with service interruptions in the Halfin–Whitt regime

Lu, Hongyuan; Pang, Guodong; Zhou, Yuhang

doi:10.1007/s00186-015-0523-z

Cited by 10 publications

(19 citation statements)

References 26 publications

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“…It is conceivable that the results can be extended to the most general conditions on service times, but that is beyond the scope of this paper. Our approach is extended to study the total count processes for G/G/N(+G) queues in the Halfin-Whitt regime in [19] when the services are i.i.d. with a continuous distribution function.…”

Section: Literature and Contributionsmentioning

confidence: 99%

G/G/∞ queues with renewal alternating interruptions

Pang

Zhou

2016

Adv. Appl. Probab.

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We study G/G/∞ queues with renewal alternating service interruptions, where the service station experiences `up' and `down' periods. The system operates normally in the up periods, and all servers stop functioning while customers continue entering the system during the down periods. The amount of service a customer has received when an interruption occurs will be conserved and the service will resume when the down period ends. We use a two-parameter process to describe the system dynamics:Xr(t,y) tracking the number of customers in the system at timetthat have residual service times strictly greater thany. The service times are assumed to satisfy either of the two conditions: they are independent and identically distributed with a distribution of a finite support, or are a stationary and weakly dependent sequence satisfying the ϕ-mixing condition and having a continuous marginal distribution function. We consider the system in a heavy-traffic asymptotic regime where the arrival rate gets large and service time distribution is fixed, and the interruption down times are asymptotically negligible while the up times are of the same order as the service times. We show the functional law of large numbers and functional central limit theorem (FCLT) for the processXr(t,y) in this regime, where the convergence is in the space 𝔻([0,∞), (𝔻,L1)) endowed with the SkorokhodM1topology. The limit processes in the FCLT possess a stochastic decomposition property.

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Section: Literature and Contributionsmentioning

confidence: 99%

G/G/∞ queues with renewal alternating interruptions

Pang

Zhou

2016

Adv. Appl. Probab.

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“…23) for some constant K > 0 depending only on p and C. The same bound holds for 0 ≤ t < s ≤ T by defining a semimetric d t,s symmetrically.Proof. By(4.20) in Theorem 4.3, we have…”

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confidence: 86%

“…That approach was first developed by Krichagina and Puhalskii [18] for G t /GI/∞ queues, and has recently further developed to study two-parameter processes in [33] for G t /GI/∞ queues and in [35,36] for G t /G/∞ queues with weakly dependent service times satisfying the φ-mixing condition. It has also been used to study G/GI/N (+GI) queues in [38,39,26,23], G t /M/N t + GI queues in [22] and overloaded G/M/N + GI queues in [12]. Although it has been by far regarded as a standard approach to study infinite-server (many-server) queues, it fails to work for the G t /G t /∞ queues with arrival dependent service times, due to the dependence structure among the service times.…”

Section: Introductionmentioning

confidence: 99%

Two-parameter process limits for an infinite-server queue with arrival dependent service times

Pang

Zhou

2017

Stochastic Processes and their Applications

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We study an infinite-server queue with a general arrival process and a large class of general time-varying service time distributions. Specifically, customers' service times are conditionally independent given their arrival times, and each customer's service time, conditional on her arrival time, has a general distribution function. We prove functional limit theorems for the two-parameter processes X e (t, y) and X r (t, y) that represent the numbers of customers in the system at time t that have received an amount of service less than or equal to y, and that have a residual amount of service strictly greater than y, respectively. When the arrival process and the initial content process both have continuous Gaussian limits, we show that the two-parameter limit processes are continuous Gaussian random fields. In the proofs, we introduce a new class of sequential empirical processes with conditionally independent variables of non-stationary distributions, and employ the moment bounds resulting from the method of chaining for the two-parameter stochastic processes.

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“…Balcioglu et al (2007) approximate a GI/D/1 queue with correlated server breakdowns by the corresponding system with an interruption process with (independent) hyper-exponential on-times and general off-times. Lu et al (2016) study the G/GI/N multiserver queue with interruptions in the Halfin-Whitt regime, that is, when the arrival rate and the number of servers are sent to infinity, while Pang and Zhou (2016) consider a G/G/∞ queueing model with server interruptions.…”

Section: 2mentioning

confidence: 99%

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Fiems

Vuyst

2018

International Journal of Applied Mathematics and Computer Science

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We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive M X +G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

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$$G/{ GI}/N(+{ GI})$$ queues with service interruptions in the Halfin–Whitt regime

Cited by 10 publications

References 26 publications

G/G/∞ queues with renewal alternating interruptions

G/G/∞ queues with renewal alternating interruptions

Two-parameter process limits for an infinite-server queue with arrival dependent service times

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

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