Tandem queues with impatient customers

Wang, Jianfu; Abouee‐Mehrizi, Hossein; Baron, Opher; Berman, Oded

doi:10.1016/j.peva.2019.102011

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…We refer the reader to [49,50] for a recent review of this literature. More recently, Wang et al [47] and Rastpour et al [39] analyze multi-server Markovian queues with abandonments. Viewed as a level-dependent quasi-birth and death process, Wang et al [47] analyze a multi-server tandem queue with abandonments where the second phase of service has a finite number of servers.…”

Section: Brief Summary Of the Related Literaturementioning

confidence: 99%

Scheduling servers in a two-stage queue with abandonments and costs

Zayas‐Cabán¹,

Cochran

2022

Prob. Eng. Inf. Sci.

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We consider the assignment of servers to two phases of service in a two-stage tandem queueing system when customers can abandon from each stage of service. New jobs arrive at both stations. Jobs arriving at station 1 may go through both phases of service and jobs arriving at station 2 may go through only one phase of service. Stage-dependent holding and lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations are developed that minimize discounted expected and long-run average costs. Because uniformization is not possible, we use the continuous-time framework and sample path arguments to analyze control policies. Our main results are conditions under which priority rules are optimal for the single-server model. We then propose and evaluate threshold policies for allocating one or more servers between the two stages in a numerical study. These policies prioritize a phase of service before “switching” to the other phase when total congestion exceeds a certain number. Results provide insight into how to adjust the switching rule to significantly reduce costs for specific input parameters as well as more general multi-server situations when neither preemption or abandonments are allowed during service and service and abandonment times are not exponential.

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Section: Brief Summary Of the Related Literaturementioning

confidence: 99%

Scheduling servers in a two-stage queue with abandonments and costs

Zayas‐Cabán¹,

Cochran

2022

Prob. Eng. Inf. Sci.

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“…A tandem queue is a queuing system organized in the series queue in which service facilities provide services in sequence [1][2][3][4]. Since Jackson [5] introduced the analytical frameworks of interconnected queues, tandem queuing systems have been extensively analyzed due to their applicability across various sectors (such as communication, transportation, manufacturing, networks) [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

Xu,

Liu

2024

Mathematics

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This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.

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“…The M/M/1 vacation two-phase queueing model with server start up, time-out, and breakdowns was examined by Ankamma Rao et al [22] . In their research, Jianfu Wang et al [23] explored a tandem queueing network that involved customers with limited patience. They utilized a Markovian framework to construct a model known as a level-dependent quasi-birth-and-death (LDQBD) process.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Rdx Mechanism in Data Transmission Using Ibm Web Sphere, Ai and Tandem Queue

NIRANJAN,

LATHA

2024

Preprint

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In this paper we have discussed tandem queue with two service nodes. In this system, the customer require services at both nodes elaborated RDX mechanism and IBM web sphere in artificial intelligence (AI). The first essential service (FES) starts in data search and initiating the data to be required in using the RDX mechanism then the second essential service (SES) starts from validating the information in IBM web sphere and insight with the use of AI. After the completion of a service at node1 if the minimum number of customer is less than ‘a’ then the server leaves for secondary job. The service started once the vacation reaches the threshold value. When the service ends at node 1, it departs from here to proceed node 2 and receive the second service from there. We have to find PGF of a queue size at an arbitrary time epoch by using supplementary variable technique. Various characteristics of the queueing system are also obtained with a numerical solution.

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Tandem queues with impatient customers

Cited by 11 publications

References 24 publications

Scheduling servers in a two-stage queue with abandonments and costs

Scheduling servers in a two-stage queue with abandonments and costs

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

Performance Analysis of Rdx Mechanism in Data Transmission Using Ibm Web Sphere, Ai and Tandem Queue

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