On the time-dependent occupancy and backlog distributions for the <i>GI</i>/<i>G</i>/∞ queue

Ayhan, Hayriye; Limón-Robles, Jorge; Wortman, Martin

doi:10.1239/jap/1032374471

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Observe however that E 0 [1(X 0 ≥ k)X 0 (X 0 − 1) · · · (X 0 − k + 1)] = φ (k) (1). This yields the following basic relationship:…”

Section: Renewal Arrivals and Exponential Service Times: The System Gmentioning

confidence: 99%

“…More specifically, infinite server queues with batch arrivals have been considered in [14], [7], [8], [9], [10]. We also mention the time-varying systems considered in [5] and [1] as well as the network of queues considered in [11]. Finally, in [13] and [12] the reader can also find results regarding matrix analytic techniques for the numerical computation of performance characteristics.…”

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confidence: 99%

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Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

Zazanis

2004

Queueing Systems

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We analyze an infinite-server queueing model with synchronized arrivals and departures driven by the point process {T n } according to the following rules. At time T n , a single customer (or a batch of size β n ) arrives to the system. The service requirement of the ith customer in the nth batch is σ i,n . All customers enter service immediately upon arrival but each customer leaves the system at the first epoch of the point process {T n } which occurs after his service requirement has been satisfied. For this system the queue length process and the statistics of the departing batches of customers are investigated under various assumptions for the statistics of the point process {T n }, the incoming batch sequence {β n }, and the service sequence {σ i,n }. Results for the asymptotic distribution of the departing batches when the service times are long compared to the interarrival times are also derived. Consider a system where groups (or batches) of customers arrive at the epochs of a point process {T n ; n ∈ Z} defined on the whole real line. The nth group arrives at time T n and consists of β n customers. The ith customer of the nth group, which we will denote by C i,n , 1 ≤ i ≤ β n , n ∈ Z, remains in the system for σ i,n time units, and then departs at the next arrival point after his serviceIn more descriptive terms we envision a shuttle bus which arrives at a certain facility at the epochs {T n } of a stationary and ergodic point process. Each time the shuttle bus arrives, it brings along a new group of passengers and delivers them to the facility. The ith passenger of the nth group will stay in this facility for σ i,n time units, and then he will move on to a waiting area from where he will be picked up by the first shuttle that arrives. We assume that the facility, the waiting area, and the shuttle, all have infinite capacity so that a new group of passengers can always be delivered to the 1

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“…Observe however that E 0 [1(X 0 ≥ k)X 0 (X 0 − 1) · · · (X 0 − k + 1)] = φ (k) (1). This yields the following basic relationship:…”

Section: Renewal Arrivals and Exponential Service Times: The System Gmentioning

confidence: 99%

mentioning

confidence: 99%

Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

Zazanis

2004

Queueing Systems

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“…The integral equations given in Corollary 1 and Corollary 2 can be solved numerically similar to the approach used by Ayhan, Limon-Robles, and Wortman [1]. The time-dependent total remaining warranty coverage time distribution (conditioned on T 0 ) is shown in Figure 1.…”

Section: Numerical Examplementioning

confidence: 99%

Stochastic modeling for computational warranty analysis

Wortman

Elkins

2005

Naval Research Logistics

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Abstract:We examine two key stochastic processes of interest for warranty modeling: (1) remaining total warranty coverage time exposure and (2) warranty load (total items under warranty at time t). Integral equations suitable for numerical computation are developed to yield probability law for these warranty measures. These two warranty measures permit warranty managers to better understand time-dependent warranty behavior, and thus better manage warranty cash reserves.

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TheG/G/sQueue

Breuer

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article provides a literature survey on results for the G/G/s multiserver queue with general interarrival and service time distributions. It further presents two fundamental aspects in a concise yet relatively self‐sufficient form. These are results on the waiting time vectors, derived by Kiefer and Wolfowitz, and the special case of the G/M/s queue with exponential service time distributions, first analyzed by Kendall.

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On the time-dependent occupancy and backlog distributions for the GI/G/∞ queue

Cited by 4 publications

References 11 publications

Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

Stochastic modeling for computational warranty analysis

TheG/G/sQueue

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