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Page 9198 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
Summary: “This paper considers a heterogeneous M/G/2 queue. The service times at server | are exponentially distributed, and at server 2 they have a general distribution B(-).  ...  (NL-EIND; Eindhoven) Waiting-time asymptotics for the \//G/2 queue with heterogeneous servers. (English summary) Queueing Syst. Theory Appl. 40 (2002), no. 1, 5-31.  ... 

Mathematical Modeling in Heavy Traffic Queuing Systems

Sulaiman Sani, Onkabetse A. Daman
2014 American Journal of Operations Research  
In addition, the diffusion approximation can conveniently model performance characters such as the queue length or the waiting time distributions in these systems.  ...  Initially, we reviewed the onset of asymptotic modeling for heavy traffic single server queuing systems and then proceeded to multi server models supporting diffusion approximations developed recently.  ...  Acknowledgements The authors are grateful to Prof. Sivasamy, R., of the Statistics Department, University of Botswana for his suggestions, corrections and editing this article.  ... 
doi:10.4236/ajor.2014.46033 fatcat:kqrjiqahdnejjeiyxhmvhzy5l4

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O.J. Boxma, Q. Deng, A.P. Zwart
2012 Queueing systems  
Introduction This paper considers a heterogeneous M / G/2 queue. Customers arrive according to a Poisson process with rate A.  ...  The above interpretation shows an interesting feature of this model: Conclusion The main results of our study of the heterogeneous M / G/2 queue with one exponential and one general server are: (i)  ... 
doi:10.1023/a:1017913826973 fatcat:3iifohm2m5c67cyqbhdc2gdao4

Page 4694 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
M/G/2 queue, and the distribution of U2(t) — U;(t) closely related to the tail of the service time den- sity.  ...  For example, if the sequence of ordered pairs of interarrival time and waiting times is strictly stationary and satisfies a joint CLT, then the queue-length process also obeys a CLT with a related limiting  ... 

The Finite-Skip Method for Multiserver Analysis [article]

Isaac Grosof, Mor Harchol-Balter, Alan Scheller-Wolf
2022 arXiv   pre-print
This class includes many important models, including the heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the threshold parallelism model, and the multiserver-job model under a  ...  Multiserver queueing systems are found at the core of a wide variety of practical systems.  ...  Previous work was only able to analyze simpler settings, such as the M/M/k and the M/(M+G)/2. In Fig. 2, we show a heterogeneous M/G/k with = 4 servers, where the server speeds vary by a factor of 4.  ... 
arXiv:2109.12663v2 fatcat:cpqzcycjava43lcf4qnr276cvi

Stochastic Analysis and Optimization of Multiserver Systems [chapter]

Mark S. Squillante
2010 Run-time Models for Self-managing Systems and Applications  
Our primary focus is on multiserver systems in general, since this research provides the mathematical methods and results that have been and will continue to be used for the stochastic analysis and/or  ...  Motivated by emerging trends and applications such as autonomic computing, this paper presents an overview of some research in the stochastic analysis and optimization of multiserver systems.  ...  Acknowledgements The author especially thanks Danilo Ardagna and Li Zhang for their kind invitation to write this paper.  ... 
doi:10.1007/978-3-0346-0433-8_1 fatcat:7ddyzwfwebhfrdkb5in4ylkcee

Analysis of a discrete-time single-server queue with an occasional extra server

Herwig Bruneel, Sabine Wittevrongel
2017 Performance evaluation (Print)  
We consider a discrete-time queueing system having two distinct servers: one server, the "regular" server, is permanently available, while the second server, referred to as the "extra" server, is only  ...  For this queueing model, we are able to derive closed-form expressions for the steadystate probability generating functions (pgfs) and the expected values of the numbers of customers in the system at various  ...  Acknowledgement This research has been partly funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (BelSPO), Belgium.  ... 
doi:10.1016/j.peva.2017.08.009 fatcat:okbjkvujgzggta4o45fc7vusye

A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows

Sem Borst, Bert Zwart
2003 Advances in Applied Probability  
The prefactor represents the probability that the heavy-tailed flows have sent at their peak rate for more than a certain amount of time, which may be interpreted as the 'time to overflow' for the light-tailed  ...  We determine the exact large-buffer asymptotics for a mixture of light-tailed and heavy-tailed input flows.  ...  The interplay of light-tailed and heavy-tailed large deviations is reminiscent of that for an M/G/2 queue with heterogeneous servers as described in [lOJ.  ... 
doi:10.1017/s0001867800012544 fatcat:4nv6cfcdofcsvhovfeoxqlyowq

Asymptotic dimensioning of stochastic service systems [article]

Britt W.J. Mathijsen
2017 arXiv   pre-print
Think of check-in lines at airports, waiting rooms in hospitals or queues in supermarkets, where the scarce resource is human manpower.  ...  efficiently utilizes the expensive resources, while at the same time, the level of service, experienced by customers, remains high.  ...  Acknowledgments The completion of this thesis would not have been possible without the many people who have supported and encouraged me along the way. I take this opportunity  ... 
arXiv:1706.09440v1 fatcat:5gdlxwszlbfr3nlajd46sjwhxm

Page 1659 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(with Metwally, S. A.; Kamel, E. A.) Distribution of the busy period in a controllable M/G/2 queue with (0, K, N, M) policy.  ...  (English summary) — Discrete-time Geo* /G/1 queue with preemptive resume priority. (English summary) Leemans, Herlinde Provable bounds for the mean queue lengths in a heterogeneous priority queue.  ... 

Page 900 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
The two repairmen problem: a finite source M/G/2 queue. 88e:60115 (with Matkowsky, B. J.; Schuss, Z.; Tier, C.) Asymptotic expansions for a closed multiple access system. 88g:60227 Kolev, N. V.  ...  Open queueing networks with bounded waiting time in the queues. (Russian.  ... 

Queues with regular variation [article]

Deng, Q (Qing), Boxma, OJ (Onno), Borst, SC (Sem = Simon)
2001
Chapter 6 The M/G/2 queue with heterogeneous servers Introduction In this chapter we consider a heterogeneous M/G/2 queue. Customers arrive according to a Poisson process with rate λ.  ...  at both queues, (iii) the cyclic polling system with Poisson input processes, and (iv) the M/G/2 queue with heterogeneous servers.  ...  at both queues, (iii) the cyclic polling system with Poisson input processes, and (iv) the M/G/2 queue with heterogeneous servers.  ... 
doi:10.6100/ir547197 fatcat:ayqlv6qs7bbc3c4cyh3io7qsfa

Page 1617 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(English summary) 2002f:60174 — (with Deng, Qing”; Zwart, Albertus Petrus) Waiting-time asymptotics for the M/G/2 queue with heterogeneous servers.  ...  (with Mitrani, 1.; Robert, Philippe) Large scale and heavy traffic asymptotics for systems with unreliable servers. (English summary) 2002b:60159 Deng, Qing? *& Queues with regular variation.  ... 

Page 1628 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
On the busy period distribution of the M/G/2 queueing system. 91k:60109 Willie, Helmut Individual blocking probabilities in the loss system G, + --- + Gy/M/1/0. 91f:60180 Winsten, C. B.  ...  theorems for queues and waiting times in multichannel, multiple-server systems under heavy traffic.  ... 

Page 490 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Ein Warteschl y mit zeitabhangigen Parametern. 80¢:60106 Hiramatsu, Toshiaki See Nishida, Toshio, 80m:60097 Hokstad, Per On the steady-state solution of the M/G/2 queue. 80f:60082 Husainov, Ja. M.  ...  Further results for the queueing system M* /M/c. 80d:60127 Danieljan, E. A. (with Zemljanoi, N. S.) On the asymptotics of the queue length of the M,\G,|1|oo system in heavy traffic. (Russian.  ... 
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