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Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains

Vinod Sharma
1997 Advances in Applied Probability  
If the original process is customer (time) stationary then so are the approximating processes. Also, the moments in the stationary case converge.  ...  For discrete arrival sequences (to a queue) which are modulated by a countable state Markov chain we form a different sequence of approximating arrival streams by which, unlike in the Asmussen and Koole  ...  Observe that Again by [13] , p. 270, Now apply this to the last equality, and again use [13] , p. 270, to obtain  ... 
doi:10.2307/1427853 fatcat:ggmmbkgjiffehg3he26ok6jyii

Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains

Vinod Sharma
1997 Advances in Applied Probability  
If the original process is customer (time) stationary then so are the approximating processes. Also, the moments in the stationary case converge.  ...  For discrete arrival sequences (to a queue) which are modulated by a countable state Markov chain we form a different sequence of approximating arrival streams by which, unlike in the Asmussen and Koole  ...  Observe that Again by [13] , p. 270, Now apply this to the last equality, and again use [13] , p. 270, to obtain  ... 
doi:10.1017/s0001867800048011 fatcat:ldpue4oqdje2lisg7v5k77jnjm

STATIONARY DISTRIBUTION CONVERGENCE FOR A MULTICLASS SINGLE-SERVER QUEUE IN HEAVY TRAFFIC

Toshiyuki Katsuda
2012 Scientiae mathematicae Japonicae  
For a multiclass single-server queue, we obtain the tightness of stationary scaled workload to show that state-space collapse occurs in the heavy-traffic regime in stationarity, from which the desired  ...  In the author's recent paper [11] , it is established that in a multiclass single-server queue with regular service disciplines, the stationary distributions and their moments for workload as well as for  ...  The key to their proof is to show that state-space collapse occurs in the heavy-traffic regime in stationarity under the assumption of tightness on the stationary workload (or stationary queue length)  ... 
doi:10.32219/isms.75.3_317 fatcat:2h3tzj4mwvh4zpxh5vqch6jbp4

Page 1235 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
, then the censored continuous time Markov chain with state space S’ and transition rates gs has a stationary distribution that is the truncated distribution of z on S’.  ...  n(x) s- gj(x,y) = a n(y)q;(y, x). yes ves This leads to Lemma 2.3: If a continuous time Markov chain with transition rates g and state space S has stationary distribution m and it satisfies local balance  ... 

On the quasi-stationary distribution for queueing networks with defective routing

Richard J. Boucherie
1997 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
This note introduces quasi-local-balance for discrete-time Markov chains with absorbing states.  ...  From quasi-local-balance product-form quasi-stationary distributions are derived by analogy with product-form stationary distributions for Markov chains that satisfy local balance.  ...  Boucherie has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.  ... 
doi:10.1017/s0334270000000795 fatcat:uyvkfuvkb5hjhplbitvj3oo2jq

Page 8566 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
., a message in the queue is allocated if its throughput is less than the available band- width at that time and none of the other messages before it in the queue can be transmitted.  ...  vector transform of the queue length and the remaining service time.  ... 

Heredity of stationary and reversible stochastic processes

Richard F. Serfozo
1986 Advances in Applied Probability  
When a stochastic process (a random measure, set, field, etc. on a group) is stationary, ergodic, or reversible, then certain functions of this process inherit these properties.  ...  of that queue over time.  ...  Thepreceding results readily extend to time and space transformations h-, . -,, .-.-. -, . -. ;..';. . ... ,.; .'.. :,'', -. -.. '--. , t t then Z is stationary.  ... 
doi:10.2307/1427313 fatcat:hd2c6iinazezhb7an7qmlg2dta

Page 353 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
It is well known that the arrival process must not be Poisson for having coincidence of time-stationary and customer-stationary queueing characteristics.  ...  The author considers a modification of the standard G/G/1 queue with unlimited waiting room and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly  ... 

Page 8423 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Further we provide recursion for- mulas to compute the stationary joint queue length distribution and the stationary distribution representing from which stream each customer in the queue arrived.” 2002k  ...  A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a  ... 

Relationships in stationary jump processes with countable state space and their applications to queues

Masakiyo Miyazawa, Genji Yamazaki
1992 Stochastic Processes and their Applications  
Relationships between the stationary distributions at an arbitrary time, just before and after jump instants are obtained by using conditional sojourn times in states and in sets of states.  ...  We consider a stationary continuous time process with a finite or countable state space, which is usually called a stationary pure jump process because it changes its state by jumps.  ...  Acknowledgement The authors wish to thank the referee for many suggestions and helpful comments.  ... 
doi:10.1016/0304-4149(92)90058-x fatcat:rmssjtdkuje7phtowyiwfjvw5e

Heredity of stationary and reversible stochastic processes

Richard F. Serfozo
1986 Advances in Applied Probability  
When a stochastic process (a random measure, set, field, etc. on a group) is stationary, ergodic, or reversible, then certain functions of this process inherit these properties.  ...  of that queue over time.  ...  The preceding results readily extend to time and space transformations h, <I> that are random.  ... 
doi:10.1017/s0001867800015895 fatcat:atroaib4nrbznitffjvzw7qrtu

Obtaining derivatives of stationary queue length probabilities through the matrix-geometric solution method

Wei-Bo Gong, Jie Pan, Christos G. Cassandras
1992 Applied Mathematics Letters  
in terms of the stationary queue length probabilities of the MfPH/l queues with infinite buffer capacity.  ...  In this paper, we show that using the matrix-geometric solution method we can express the derivatives of the stationary queue length probabilities of the M/PH/l/K queue or the M/PH/l/(w,K) multiclass queue  ...  and service times with phase type distributions.  ... 
doi:10.1016/0893-9659(92)90140-5 fatcat:rbqon3wb5jfs7imnx3jo5dkkni

Delay and queue lengths at stop/go control during half-width construction

L Venter, C J Bester
2015 Journal of the South African Institution of Civil Engineering  
control, but not specifically waiting time for the vehicle in the front of the stationary queue and back-of-queue position (in metres).  ...  the factors that influence the waiting time for the vehicle in the front of the stationary queue at the STOP/GO control and the backof-queue position.  ... 
doi:10.17159/2309-8775/2015/v57n4a1 fatcat:gx7gtmfohbcireqfmfsavfesja

Many-server Queues with Customer Abandonment: Numerical Analysis of their Diffusion Model

J. G. Dai, Shuangchi He
2013 Stochastic Systems  
We use a multidimensional diffusion process to approximate the dynamics of a queue served by many parallel servers. Waiting customers in this queue may abandon the system without service.  ...  With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments.  ...  The authors would like to thank Ton Dieker and Vadim Linetsky for their helpful comments on solving the basic adjoint relationship.  ... 
doi:10.1287/11-ssy029 fatcat:hw2xnacbpnaltip2m7b4yqvera

Many-server queues with customer abandonment: Numerical analysis of their diffusion model

J. G. Dai, Shuangchi He
2013 Stochastic Systems  
We use a multidimensional diffusion process to approximate the dynamics of a queue served by many parallel servers. Waiting customers in this queue may abandon the system without service.  ...  With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments.  ...  The authors would like to thank Ton Dieker and Vadim Linetsky for their helpful comments on solving the basic adjoint relationship.  ... 
doi:10.1214/11-ssy029 fatcat:o4dwdft3ofau5mi5rziorpso4q
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