MAP/(PH/PH)/c Queue with Self-Generation of Priorities and Non-Preemptive Service

Krishnamoorthy, A.; Babu, S.; Narayanan, Viswanath C.

doi:10.1080/07362990802405802

Cited by 24 publications

(12 citation statements)

References 19 publications

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“…The reason to use PH distribution for fitting the arrival interval and service time in queuing system is its own apt analyticity, universality, and computability . Theoretically, it can be fit to any positive random number infinitely which has resulted in the emergence of ample PH-based queuing models including PH/PH/1 by Krishnamoorthy et al (2008) and PH/PH/1/C by Alfa and Zhao (2000). In the transportation domain, Hu et al 2013 for the first time applied the PH distribution to fit the passengers' flow arrival interval distribution at urban rail transit station which has revealed a good data fitting effect.…”

Section: Literature Reviewmentioning

confidence: 99%

A new simulation-optimization approach for the circulation facilities design at urban rail transit station

Khattak

Jiang

Zhu

et al. 2017

AoT

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Width design of the urban rail transit stations circulation facilities is a vital issue. The existing width design approach failed in fully considering the essential factors such as fluctuation in passengers’ arrival process, fluctuation and state-dependence in passengers walking speed and the blocking when passengers’ demand exceeds the capacity of facilities. For this purpose, a PH-based simulation-optimization approach is proposed that fully considers the fluctuation, the state-dependence, Level of Service (LOS) and blocking effect. This novel approach provides automatic reconfiguration of the widths of circulation facilities by a concurrent implementation of a PH-based Discrete-Event Simulation (DES) model and the Genetic Algorithm (GA). The proposed PH-based simulation- optimization approach and the existing design approaches based on the exponential and deterministic models are applied to design the widths of circulation facilities. The results reveal that the circulation facilities designed by the proposed approach have larger widths. Similarly, increase in the SCV of arrival interval results in increasing the widths designed by the proposed approach increase while the widths of the other two approaches stay the same. The width designed of the proposed approach increase at faster rate than that of the other two approach when the passengers’ arrival rate increases.

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Section: Literature Reviewmentioning

confidence: 99%

A new simulation-optimization approach for the circulation facilities design at urban rail transit station

Khattak

Jiang

Zhu

et al. 2017

AoT

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“…Short review of the recent papers related to this subject can be found in [9] where a multiserver queue with quite involved mechanisms of servers breakdowns and repair is analyzed with emphasis to evaluation of survivability of the system. In [10][11][12], multiserver queues with nonpreemptive priorities are investigated. Model in [12] assumes self-generation of priorities.…”

Section: Introductionmentioning

confidence: 99%

MAP+MAP/M2/N/∞Queueing System with Absolute Priority and Reservation of Servers

Sun

Lee

Dudin

et al. 2014

Mathematical Problems in Engineering

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We consider a multiserver queueing system with an infinite buffer and two types of customers. The flow of customers is described by two Markovian arrival processes (MAPs). Type 1 customers have absolute priority over type 2 customers. If the arriving type 1 customer encounters all servers busy, but some of them provide service to type 2 customers, service of one type 2 customer is terminated and type 1 customer occupies the released server. To avoid too frequent termination of service of type 2 customers, we suggest reservation of some number of servers for type 1 customers. Type 2 customers, who do not succeed to get a server upon arrival or are knocked out from a server, join the buffer or leave the system forever. During a waiting period in the buffer, type 2 customers can be impatient and may leave the system forever. The ergodicity condition of the system is derived in an analytically tractable form. The stationary distribution of the system states and the main performance measures are calculated. The Laplace-Stieltjes transform of the waiting time distribution of an arbitrary type 2 customer is derived. Numerical examples are presented. The problem of the optimal channel reservation is numerically solved.

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“…The concept of self-generation of priorities was proposed by Krishnamoorthy and Narayanan [11] and subsequently analyzed in a series of papers by Wang [26], Gómez-Corral et al [8], and Krishnamoorthy et al [12,13,14,15], most of which essentially concern a model where regular customers in a multi-server, single class queue would "selfpromote" at a constant rate while waiting, independently of other customers in the queue.…”

Section: Figure 1: Proposed Queueing Modelmentioning

confidence: 99%

“…None of the foregoing transplant papers reflected this priority aspect, which we attempt to do by invoking the idea of patients who "self promote" from regular status to priority status at an exponential rate, while waiting. The "self-promoting" literature is fairly extensive, comprising Krishnamoorthy and Narayanan [11], Wang [26], Gómez-Corral et al [8], and Krishnamoorthy et al [12,13,14,15]. In telecommunication systems, the idea of promoting packets with low priority status to the high priority queue is referred to as "priority jumps" and has been studied in the recent past as well (e.g., see Maertens et al [19], and references therein).…”

Section: Introductionmentioning

confidence: 99%

A model for deceased-donor transplant queue waiting times

et al. 2014

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In many jurisdictions, organ allocation is done on the basis of the health status of the patient, either explicitly or implicitly. This paper presents a self-promoting priority queueing model for patient waiting times which takes into account changes in health status over time. In this model, most patients arrive as "regular" customers to the queue, but as the health of a patient degrades, their status is promoted to "priority" to reflect the increased urgency of the transplant. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the marginal delay distributions for each queue are computed via the use of matrix analytic techniques. The model is calibrated using liver transplantation wait-list data, provided by a regional health centre in Canada, that tracked approximately 1,100 patients over nearly 13 years. Blood-type specific models are fit and performance measures, such as the mean and distribution of the time until transplant, are obtained and compared to empirical estimates calculated using the raw data.

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MAP/(PH/PH)/c Queue with Self-Generation of Priorities and Non-Preemptive Service

Cited by 24 publications

References 19 publications

A new simulation-optimization approach for the circulation facilities design at urban rail transit station

A new simulation-optimization approach for the circulation facilities design at urban rail transit station

MAP+MAP/M2/N/∞Queueing System with Absolute Priority and Reservation of Servers

A model for deceased-donor transplant queue waiting times

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