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A Markov Renewal Approach to M/G/1 Type Queues with Countably Many Background States

Masakiyo Miyazawa
2004 Queueing systems  
Usually, matrix analysis is extensively used for studying the M/G/1 type queue. However, this may not be convenient when the background states are countable.  ...  Those results are applied to study the tail decay rates of the stationary distributions. This includes refinements of the existence results with extensions.  ...  In those papers, the stationary distribution of the conventional M/G/1 type queue is shown to be a Markov renewal function (also see Section 3.2).  ... 
doi:10.1023/b:ques.0000021148.33178.0f fatcat:4ni4wtkwkfh3djssrimk2dr5w4

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Dieter Fiems, Stijn De Vuyst
2018 International Journal of Applied Mathematics and Computer Science  
We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations.  ...  By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system.  ...  If not, the server leaves for another vacation of random duration; see, e.g., the works of Doshi (1986) , Takagi (1991) or Tian and Zhang (2006) for references to M/G/1-type vacation models.  ... 
doi:10.2478/amcs-2018-0053 fatcat:l5yqze5x3nhtzlooz2otdi6nou

On a M/G/1 Queue Subject to Random Breakdowns with General Repair Times and Server's Choice for Deterministic or General Server Vacations

2019 Advances in Natural and Applied Sciences  
We study an M/G/1 Type queueing system subject to random failures.  ...  If the server chooses to take a vacation, he has the option of taking a deterministic vacation of constant duration or a general vacation of random length of time.  ...  Many meaningful and exciting results are derived cases 1 to 6. Hopefully, these new results will be an excellent addition to the literature of queueing theory.  ... 
doi:10.22587/anas.2019.13.2.1 fatcat:bz6egil4bjcj7hrnx2hwnbgbwi

On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations

Martyna Kobielnik, Wojciech Kempa
2021 Sensors  
A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed.  ...  Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses.  ...  A M/G/1-type queueing model with single working vacations and vacation interruption under a Bernoulli schedule was considered in [15] .  ... 
doi:10.3390/s21165507 pmid:34450948 pmcid:PMC8400104 fatcat:ir44oxzww5d4vhihtxmy44de2i

Steady-state analysis of a discrete-time batch arrival queue with working vacations

Ji-hong Li, Wei-qi Liu, Nai-shuo Tian
2010 Performance evaluation (Print)  
We formulate the system as an embedded Markov chain at the departure epoch and by the M/G/1-type matrix analytic approach, we derive the probability generating function (PGF) of the stationary queue length  ...  This paper analyzes a discrete-time batch arrival queue with working vacations.  ...  Acknowledgements The authors would like to thank editors and three referees for their valuable comments and suggestions, which were very helpful to improve the paper.  ... 
doi:10.1016/j.peva.2010.03.001 fatcat:hnnk3hy3tvacdag3xsuadnqone

Page 5954 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
An arrival time approach (ATA) to find the queue length distri- butions for M/G/1-type queues with generalized server vacations is proposed.  ...  [Ahn, Chang-Won] An arrival time approach to /M/G/|-type queues with generalized vacations. (English summary) Queueing Syst. Theory Appl. 38 (2001), no. 1, 91-100.  ... 

Stochatic Decomposition Result of an Unrelaible Queue with Two Types of Services

Gautam Choudhury, Akhil Goswami, Anjana Begum, Hemanta Kumar Sarmah
2020 Mathematics and Statistics  
Our intention is to look into some sort of united approach to establish stochastic decomposition result for two types of general heterogeneous service queues with generalized vacations for unreliable server  ...  of system (queue) size with no vacation and additional system (queue) size due to vacation.  ...  Infact, the notion of generalized vacation was first introduced by Fuhrmann and Cooper's for an M/G/1 type of model in order to generalize results of many existing vacation models of M/G/1 type.  ... 
doi:10.13189/ms.2020.080219 fatcat:6fpnkpahzvdi3pilmyu2qdxfnm

Characterizing the BMAP/MAP/1 Departure Process via the ETAQA Truncation

Qi Zhang, Armin Heindl, Evgenia Smirni
2005 Stochastic Models  
The departure process of a BMAP/MAP/1 queue is also given exactly by a MAP with an infinite number of states, which is obtained by filtration of the M/G/1-type process that models the BMAP/MAP/1 queue.  ...  Exploiting its full generality, one can apply the ETAQA methodology for the solution of M/G/1-type processes [16] to characterize the departure process of the BMAP/MAP/1 queue.  ...  M/G/1-type processes and ETAQA A BMAP/MAP/1 queue defines an M/G/1-type Markov process.  ... 
doi:10.1081/stm-200056221 fatcat:vy6pb4x3fnhqxdvqiho37wikbm

Page 4200 of Mathematical Reviews Vol. , Issue 95g [page]

1995 Mathematical Reviews  
The authors emphasize that the formulas for this queue are natural matrix analogues of those for the M/G/1 type queue.  ...  By using the notion of a rate conservation law, a general approach is obtained for deriving decomposition formulas for characteristics of queues with server vacations.  ... 

Page 1705 of Mathematical Reviews Vol. , Issue 90C [page]

1990 Mathematical Reviews  
Several basic algorithms for the computation of the state probabilities and waiting time probabilities are discussed for M/G/1 type queues which include those with batch arrivals.  ...  Summary: “We consider M/G/1 bulk arrival queues with server vacations.  ... 

Page 5087 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
Summary: “In this paper, we study both the G//M/1 type and the M/G/1 type Markov chains with the special structure Ay = wf.  ...  We regard the model with two types of MAP arrivals as an MAP/SM/1 queue with only nonpriority customers arrivals, semi-Markovian service times and some server vacations.  ... 

Page 3563 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
The authors consider a single-server queueing system of M/G/1 type with the following service policy.  ...  The vacation time may be considered as the time period required to release an SVC or as the time during which the server goes to set up other SVCs.  ... 

Page 4784 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
An embedded Markov chain of M/G/1 type with a tree structure allows conditions for ergodicity to be given.  ...  vacation scheme in which the server always waits for an arriving customer when he finds an empty queue upon returning from a vacation.  ... 

Page 5047 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
More recently, Shanthikumar has generalized some of the results to M/G/1 type queues in which the arrival pattern during the vacations may be different from that dur- ing the time the server is actually  ...  We also provide an alternative approach to deriving Shanthikumar’s results for queue length at departure epochs.” 91i1:60241 60K25 90B22 Farahmand, K.  ... 

Page 3011 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
The results are certainly interesting in the sense that the M/G/1- type queue with structured arrivals can be solved in the same way as the M/GI/1 queue by using the supplementary variable method.  ...  The service times are assumed to be general i.i.d. random variables.  ... 
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