Loss Systems with Slow Retrials in the Halfin–Whitt Regime

Avram, Florin; Janssen, Ajem Guido; Leeuwaarden, Johan S. H. van

doi:10.1017/s0001867800006273

Cited by 8 publications

(30 citation statements)

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“…Then, ignoring the fact that service times are the sum of two exponentials rather than exponential, Cohen's equation (equation 1in Avram, Janssen, and Van Leeuwaarden (2013)) implies that the re-entry rate is the unique root Ω to…”

Section: Discussionmentioning

confidence: 99%

A Continuous-Class Queueing Model With Proportional Hazards-Based Routing

et al. 2018

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Section: Discussionmentioning

confidence: 99%

A Continuous-Class Queueing Model With Proportional Hazards-Based Routing

et al. 2018

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“…Asymptotic analysis for the case of large number of servers may be the topic of any future research. In this direction, Avram et al [27] consider the blocking probability under slow retrials and Halfin-Whitt regime.…”

Section: Blocking Probability Versus Number Of Serversmentioning

confidence: 99%

Multiserver Queue with Guard Channel for Priority and Retrial Customers

Kajiwara

Phung-Duc

2016

International Journal of Stochastic Analysis

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This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.

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“…This paper builds on several results obtained in [2]. Compared to earlier studies [2], [8], [11], [12], and [14], the system in this paper brings about additional mathematical challenges, because of the effects of rejection and reattempts. In short, we make the following contributions: (i) We consider two stationary performance measures: the probability that an arriving customer finds all servers occupied D F (s, λ), and the probability that an arriving customer is rejected D R F (s, λ).…”

mentioning

confidence: 91%

“…The analysis in this paper for a model with retrials and admission control is performed in a similar spirit as was performed for the Erlang C model [8], [12], the Erlang B model [11], and the Erlang A model (with abandonments) [14]. In the recent paper [2] on a many-server system with retrials, the admission control policy that rejects all delayed customers (loss system) was analyzed. This paper builds on several results obtained in [2].…”

mentioning

confidence: 99%

“…In the recent paper [2] on a many-server system with retrials, the admission control policy that rejects all delayed customers (loss system) was analyzed. This paper builds on several results obtained in [2]. Compared to earlier studies [2], [8], [11], [12], and [14], the system in this paper brings about additional mathematical challenges, because of the effects of rejection and reattempts.…”

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confidence: 99%

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Staffing Many-Server Systems with Admission Control and Retrials

Janssen¹,

Leeuwaarden²

2015

Advances in Applied Probability

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We consider Markovian many-server systems with admission control operating in a Quality-and-Efficiency-Driven (QED) regime, where the relative utilization approaches unity while the number of servers grows large, providing natural Economies-of-Scale. In order to determine the optimal admission control policy, we adopt a revenue maximization framework, and suppose that the revenue rate attains a maximum when no customers are waiting and no servers are idling. When the revenue function scales properly with the system size, we show that a nondegenerate optimization problem arises in the limit. Detailed analysis demonstrates that the revenue is maximized by nontrivial policies that bar customers from entering when the queue length exceeds a certain threshold of the order of the typical square-root level variation in the system occupancy. We identify a fundamental equation characterizing the optimal threshold, which we extensively leverage to provide broadly applicable upper/lower bounds for the optimal threshold, establish its monotonicity, and examine its asymp-totic behavior, all for general revenue structures. For linear and exponential revenue structures, we present explicit expressions for the optimal threshold.

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Loss Systems with Slow Retrials in the Halfin–Whitt Regime

Cited by 8 publications

References 10 publications

A Continuous-Class Queueing Model With Proportional Hazards-Based Routing

A Continuous-Class Queueing Model With Proportional Hazards-Based Routing

Multiserver Queue with Guard Channel for Priority and Retrial Customers

Staffing Many-Server Systems with Admission Control and Retrials

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