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The Busy Period of an M/G/1 Queue with Customer Impatience

Onno Boxma, David Perry, Wolfgang Stadje, Shelley Zacks
2010 Journal of Applied Probability  
We consider an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience  ...  We determine the busy period distribution for various choices of the patience time distribution. The main cases under consideration are exponential patience and a discrete patience distribution.  ...  Section 5 2 An integral equation Model description Let {V (t), t ≥ 0} denote the virtual waiting time (the load) of an M/G/1 queue with arrival intensity λ.  ... 
doi:10.1239/jap/1269610821 fatcat:fudp7se3ovh3hjheo36g62uroa

The Busy Period of an M/G/1 Queue with Customer Impatience

Onno Boxma, David Perry, Wolfgang Stadje, Shelley Zacks
2010 Journal of Applied Probability  
We consider an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience  ...  We determine the busy period distribution for various choices of the patience time distribution. The main cases under consideration are exponential patience and a discrete patience distribution.  ...  Section 5 2 An integral equation Model description Let {V (t), t ≥ 0} denote the virtual waiting time (the load) of an M/G/1 queue with arrival intensity λ.  ... 
doi:10.1017/s0021900200006446 fatcat:geeomm7mkragxpfjgflwwwm52y

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation [chapter]

János Sztrik, Ádám Tóth, Elena Yu. Danilyuk, Svetlana P. Moiseeva
2021 Communications in Computer and Information Science  
In this paper, we consider a retrial queueing system of M/G/1 type with an unreliable server, collisions, and impatient customers.  ...  , the mean waiting time of an arbitrary, successfully served, impatient customer, etc.  ...  We consider a queueing system of M/G/1 with collisions, impatience of the customers, and an unreliable server which is shown in Fig. 1 .  ... 
doi:10.1007/978-3-030-72247-0_22 fatcat:3bga36eno5fvnndsap23yxjgvu

Analysis of customers' impatience in queues with server vacations

Eitan Altman, Uri Yechiali
2006 Queueing systems  
Keywords Queueing · Single and multiple vacations · Impatience · Abandonment · M/M/1 · M/G/1 · M/M/c.  ...  We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form  ...  Takacs (1974) further studied the M/G/1 queue in which customers have a fixed threshold on their sojourn time, and derived the limiting distributions of the actual and of the virtual waiting times.  ... 
doi:10.1007/s11134-006-6134-x fatcat:7sj2zj2rbfdgzlnmzmvd22nqxe

On First Come, First Served Queues with Two Classes of Impatient Customers [article]

Ivo Adan, Brett Hathaway, Vidyadhar G. Kulkarni
2018 arXiv   pre-print
We first consider an M/G/1 + M queue and then analyze the M/M/k + M case.  ...  We study systems with two classes of impatient customers who differ across the classes in their distribution of service times and patience times.  ...  Acknowledgements The authors would like to thank Marko Boon for carefully checking all calculations with Mathematica. 22 Ivo Adan et al.  ... 
arXiv:1710.03798v2 fatcat:5sa2plmkynaalbydfoasq2huyy

A simple analysis of a D/GI/1 vacation queue with impatient customers [article]

Assia Boumahdaf
2017 arXiv   pre-print
In this paper, we deal with an D/GI/1 vacation system with impatient customers.  ...  We give a sufficient condition for the existence of a limit distribution of the waiting time and integral equations are derived in both reneging and balking scenarios.  ...  The same author in [11] , derives recursive equations in the case of a deterministic service times for the steady-state distributions of the virtual waiting times in a M/G/1 queue with multiple and single  ... 
arXiv:1703.01453v1 fatcat:7yqnhusmorbelihxv3tpmm4ysm

On first-come, first-served queues with two classes of impatient customers

Ivo Adan, Brett Hathaway, Vidyadhar G. Kulkarni
2018 Queueing systems  
Keywords Call centers · Impatient customers · Virtual queueing time process · M/M/k + M queue · M/G/1 + M queue Mathematics Subject Classification 60K25 · 68M20 · 90B22  ...  We first consider an M/G/1 + M queue and then analyze the M/M/k + M case.  ...  Acknowledgements The authors would like to thank Marko Boon for carefully checking all calculations with Mathematica.  ... 
doi:10.1007/s11134-018-9592-z fatcat:sgieuivvojcu5c7jiahtzudbvu

The M/G/1+G queue revisited

Onno Boxma, David Perry, Wolfgang Stadje
2011 Queueing systems  
We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than  ...  We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs first.  ...  The waiting time in steady state Consider an M/G/1 + G w queue with arrival rate λ, service time distribution G and patience distribution H.  ... 
doi:10.1007/s11134-010-9205-y fatcat:ojzdzy6lw5frtc5zybsakosxri

On Two Priority Multi-Server Queues with Impatient Customers

Hung-Wei Li
2016 International Journal of Operations Research  
This study considers a system of multi-server queues with two classes of impatient customers: high-priority and low-priority.  ...  in order to calculate the expected waiting time for both classes of customers.  ...  Kella and Yechiali [10] used probabilistic equivalence between the M/G/1 queue with multiple server vacations and the M/M/c system, in which the Laplace-Stieltjes transform is applied to waiting times  ... 
doaj:36e6d28abf4247b6a4363774a57ff3ea fatcat:65mbinszmff47gnpayeleia2w4

On the SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers [article]

Jing Dong, Rouba Ibrahim
2021 arXiv   pre-print
priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service.  ...  We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions.  ...  [23] develop a unified framework to analyze several age-based scheduling policies in the M/G/1 queue.  ... 
arXiv:2102.05789v1 fatcat:nng23rwcpfhdzbwagcfbc44upe

Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers

Yoshiaki Inoue, Onno Boxma, David Perry, Shelley Zacks
2017 Queueing systems  
Both variants are related to an M/G/1 queue in which the service time of a customer depends on its waiting time.  ...  Our main focus is on the virtual and actual waiting times, and on the loss probability of customers.  ...  We consider batch-arrival M/G/1 queues with impatient customers.  ... 
doi:10.1007/s11134-017-9565-7 fatcat:eo62zaldybca3n7mpyvmvfrfp4

Unreliable Mx/G/1 retrial queue with multi-optional services and impatient customers

Amita Bhagat, Madhu Jain
2013 International Journal of Operational Research  
The impatient customers are allowed to balk depending upon server's status; they may also renege after waiting sometime in the queue.  ...  The present investigation deals with M x /G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair.  ...  Acknowledgements The authors are thankful to the editor and learned referees of IJOR for their worthy suggestions which helped in improving the paper and also to MHRD for providing financial assistance  ... 
doi:10.1504/ijor.2013.053614 fatcat:ed2bgsmhsjealpqwh33cadycwa

Control of G/MX/1 Queueing System with N-Policy and Customer Impatience

Si-Yeong Lim, Sun Hur
2016 Industrial Engineering & Management Systems  
We introduce a queueing system with general arrival stream and exponential service time under the N-policy, where customers may renege during idle period and arrival rates may vary according to the server's  ...  Probability distributions of the lengths of idle period and busy period are derived using absorbing Markov chain approach and a method to obtain the optimal control policy that minimizes long-run expected  ...  Swensen (1986) utilizes the remaining workload to derive the asymptotic distributions of the actual waiting time and the virtual waiting time of G/M/c queue with impatient customers when the interarrival  ... 
doi:10.7232/iems.2016.15.2.123 fatcat:hhev37cgonf3rkfh27l7guujfa

Stationary Delays for a Two-Class Priority Queue With Impatient Customers

Oualid Jouini, Yves Dallery
2007 Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools  
We consider a Markovian multiserver queue with two types of impatient customers, high and low priority ones. The first type of customers has a non-preemptive strict priority over the other type.  ...  After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time he will renege and be lost.  ...  A simpler form of the latter distribution is obtained by [10] for an M/G/1 queue. A number of approximations for the probability to abandon are developed in [4] .  ... 
doi:10.4108/valuetools.2007.2001 dblp:conf/valuetools/JouiniD07 fatcat:t3bbtwwsl5b2fn4mgp4yxthnju

Impatient customers in an M/M/c queue with single and multiple synchronous working vacations

Shakir Majid Ganie, P Manoharan
2018 Pakistan Journal of Statistics and Operation Research  
In this paper, an M/M/c queuing model with synchronous working vacation and impatient customers is considered.  ...  The M/M/c queue with two such policies is described and using the PGF method, we obtain various system performance measures in terms of two indicators.  ...  Takacs(1974) further analyzed the M/G/1 queuing system in which customers sojourn time have a static threshold and obtained the actual and virtual limiting waiting time distributions.  ... 
doi:10.18187/pjsor.v14i3.1866 fatcat:uxvbmrxd3vcqzlbl6mp5rsv2b4
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