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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. ...
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
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
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 ...
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
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
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
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
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
(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. ...
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. ...
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
(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. ...
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. ...
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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