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Some explicit formulas for mixed exponential service systems

Vernon Rego
1988 Computers & Operations Research  
We present some explicit formulas for queue length and waiting time distributions of customers in the MfHE",/l queue.  ...  I From Lemma 1, it is clear that if the service-time distribution of a singIe-server queue is  ...  INTRODUCTION For M IGIII systems in which service-time distributions are mixtures of exponentials, we present a method that enables us to obtain explicit formulas for steady-state queueing distributions  ... 
doi:10.1016/0305-0548(88)90047-0 fatcat:2asngyvnsrbcfg3xhknlqoucuq

Page 6302 of Mathematical Reviews Vol. , Issue 89K [page]

1989 Mathematical Reviews  
{For the entire collection see MR 88g:60006.} A. M. Zakharin (2-AOSUK-B) 89k:60141 60K25 90B22 Rego, Vernon (1-PURD-C) Some explicit formulas for mixed exponential service systems. Comput. Oper.  ...  For the single-server queue with Poisson arrivals and a service- time distribution which is a mixture of exponential distributions, explicit formulas for the steady-state queue length and waiting time  ... 

Queueing Systems with Random Volume Customers and their Performance Characteristics

Oleg Tikhonenko, Marcin Ziółkowski
2021 Journal of Information and Organizational Sciences  
We discuss basic problems of the theory of these systems and their performance characteristics. We also present some examples and results for systems with random volume customers  ...  The non-homogeneity we treat in the following sense: in systems under consideration, we characterize each customer by random capacity (volume) that can have an influence on his service time.  ...  We can obtain loss characteristics in explicit form for some queueing systems with random volume customers.  ... 
doi:10.31341/jios.45.1.2 fatcat:3drkbtap5zhmzbmrmp5bjsqdme

Page 5265 of Mathematical Reviews Vol. , Issue 82m [page]

1982 Mathematical Reviews  
We find the solution in an explicit form, obtaining formulas for calculating the fundamental characteristics of the system.” Valdés, José; Chernous, Konstantin (Cornous, K.  ...  A queueing system with mixed priorities. (Spanish) Investigacion Oper. No. 2-3 (1980), 103-110. From the text: “We consider a queueing system with priority and accumulation of service failures.  ... 

To Pool or Not to Pool in Call Centers

Nico M. van Dijk, Erik van der Sluis
2008 Production and operations management  
This in turn will lead to a variety of options for an optimization search, which is still highly open for scientific research.  ...  This is a question of general interest for call center management.  ...  For this trade off, however, there is no simple answer. Further research in this direction is therefore strongly suggested.  ... 
doi:10.3401/poms.1080.0029 fatcat:u2unh5bhobanni2hpayuf3lsum

Page 1128 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Further, an explicit formula for y(u) is presented for the case where p(r) is a two-step function.  ...  To demonstrate the effectiveness of our method, some numerical examples are presented for service-time distributions such as geo- metric, deterministic, arbitrary, and mixed.  ... 

Page 2211 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
For ex- ample, it is well known for the test-case class M’/M/1 that the line waiting-time DF has a generalized mixed exponential DF (see the authors’ references), with unique and possibly complex scale  ...  A two-stage exponential network with exponentially distributed in- terarrival times of the system and exponentially distributed service times in both stages is considered.  ... 

Specifying and Validating Data-Aware Temporal Web Service Properties

S. Halle, R. Villemaire, O. Cherkaoui
2009 IEEE Transactions on Software Engineering  
We show experimentally how this translation is significantly more efficient for complex formulae and makes model checking of data-aware temporal properties on real-world web service workflows tractable  ...  A "naïve" translation of CTL-FO + into CTL leads to a serious exponential blowup of the problem that prevents existing validation tools to be used.  ...  They thank Jérôme Tremblay and Boubker Ghandour for their technical contribution to this work.  ... 
doi:10.1109/tse.2009.29 fatcat:jfrk7v7vwzg3xpddxh4i3sssva

An experimental testbed to predict the performance of XACML Policy Decision Points

Bernard Butler, Brendan Jennings, Dmitri Botvich
2011 12th IFIP/IEEE International Symposium on Integrated Network Management (IM 2011) and Workshops  
Cluster characterisations are used as inputs to a PDP performance model for a given policy/request mix and an analytic (queueing) model is used to estimate the equilibrium server load for different mixes  ...  Our experiments with two XACML PDP implementations show that measured request service times are typically clustered by request type; thus an algorithm for request cluster identification is presented.  ...  ACKNOWLEDGMENTS The authors acknowledge the contribution of Keith Griffin and Ger Lawlor, Cisco Systems Inc., who helped clarify the requirements for XACML server performance.  ... 
doi:10.1109/inm.2011.5990711 dblp:conf/im/ButlerJB11 fatcat:y3yz2wtj6fgdpbsuc2lzf7eh2q

Waiting Times when Service Times are Stable Laws: Tamed and Wild [chapter]

Donald P. Gaver, Patricia A. Jacobs
1999 International Series in Operations Research and Management Science  
Send comments regarding this burden estimate o> any other aspect of this collector) of information .including suggestonsfor reducing this burden, to Washington Headquarters Services, Directorate for Information  ...  REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden tor this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions  ...  The result is a formula for every screening level K= 1/JI.  ... 
doi:10.1007/978-1-4615-5191-1_15 fatcat:inlz5ueq6bhhnjfabc3v4jei5q

Page 802 of Mathematical Reviews Vol. 32, Issue 4 [page]

1966 Mathematical Reviews  
The author considers the special cases ®(r) = pr +qr~* and ®(r)=pr"+qr~", and gives more explicit formulae in these cases.  ...  are served at a single service channel one at a time with exponential service time dis- tribution of mean »~*.  ... 

Page 4332 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
The service policy at each queue is either exhaustive or gated service, but stays the same for all visits.  ...  Based on the formula for «, a sensitivity analysis with respect to the system parameters, in particular with respect to the batch-size distribution and the simultaneity of the batch arrivals, is presented  ... 

Page 692 of Mathematical Reviews Vol. 19, Issue 6 [page]

1958 Mathematical Reviews  
The main attention in the paper is to determining equi- librium congestion probabilities for a system with Poisson arrivals, exponential service times, and a general balking distribution, although they  ...  Rus- sian and German summaries) The probability of loss and the distribution of delays are determined for a “mixed” queueing system with servers and r places for waiting customers.  ... 

Page 3828 of Mathematical Reviews Vol. , Issue 81I [page]

1981 Mathematical Reviews  
Gebiete 4 (1965/66), 316-339; MR 34 #7209] gave explicit formulas for Z, but only when p is random.  ...  The purpose of this paper is to obtain explicit formulas for Z under specific assumptions about the random arrays p and T.  ... 

Page 925 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
The Laplace transforms of the generating functions for the transient state probabilities and explicit formulas for the steady-state probabilities are obtained.  ...  Jacques Janssen (Brussels) Rosenkrantz, Walter A. (1-MA) 87b:60156 Some theorems on the instability of the exponential back-off protocol.  ... 
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