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Page 2478 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
Summary (translated from the Russian): “Consider a closed star- shaped queueing network with arbitrary distributions of service lengths in queueing systems at network nodes under certain con- straints  ...  a product-form stationary distribution or a stationary distribution which has an asymptotic product form in an appropriate limit, and Section 6 discusses output processes of single queues.  ... 

Page 3695 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
In this paper, the author continues his study of multiserver queue- ing systems with exponentially distributed service times and with interarrival times T,,,1 —T, which depend on the queue length at Tn  ...  A queueing network is considered which consists of n nodes in se- ries (i.e., “tandem connection” ) with one Poisson input at the first queue, and with a general service time distribution at each node.  ... 

Page 6740 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
This paper studies the transient behavior of a single server queue in discrete time.  ...  Summary: “In this paper, we study discrete-time priority queueing 60 PROBABILITY THEORY AND STOCHASTIC PROCESSES 6740 systems fed by a large number of arrival streams.  ... 

Page 3673 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
One result is that if a process is 96f:60157 monotone and its initial distribution is associated, then the pro- cess is associated in time.  ...  The results provide (1) a sufficient condition for ergodicity of the system and a boundary for the expected numbers of customers waiting in each queue, and (2) a random order of the stationary queue length  ... 

Page 5152 of Mathematical Reviews Vol. , Issue 89I [page]

1989 Mathematical Reviews  
The results are used to obtain distribution properties of some discrete characteristics in M/G/\ and GI/M/\ queues. B. M.  ...  Sufficient conditions for uniform monotonicity of time-discrete Markov chains are formulated in terms of transition probability matrices.  ... 

Page 808 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Summary: “This paper presents the performance analysis of a discrete-time finite-buffer queue with batch input, general interar- rival and geometric service times.  ...  Also, the queue size distribu- tion and the expected queue length are deduced. The two models are studied using supplementary variable technique.  ... 

Page 8823 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
[Ramakrishnan, Subramanian] (1-MIAM; Coral Gables, FL) Monotonicity and asymptotic queue-length distribution in discrete-time networks. (English summary) Queueing Syst.  ...  Summary: “For closed, cyclic, discrete-time networks with one server per node and with independent, geometric service times, in equilibrium, the joint queue-length distribution can be real- ized as the  ... 

Page 1768 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
The transmission time of the jobs in the channel and the time of servicing the jobs at the network nodes are random variables with exponential distributions.  ...  This generalizes previous work using N and D separately. The (N,D) model is solved in discrete time using an embedded Markov chain, and also in continuous time.  ... 

Page 4962 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
They are interested in the asymptotic prop- erties of this process when N and M grow in a good asymptotics.  ...  These customers are in the queues and are served according to the FIFO discipline at each node, and the service times at each queue form a sequence of equally distributed random variables.  ... 

Page 3283 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
tail distribution of the queue length by bounding the asymptotic decay constant.  ...  In this paper, they consider a discrete-time queue in which the arrival process is a superposition of irreducible, stationary and periodic Markov sources and obtain upper and lower bounds for the asymptotic  ... 

Page 297 of Mathematical Reviews Vol. , Issue 86a [page]

1986 Mathematical Reviews  
This observation enables us to determine (i) the stationary and lim- iting distributions (when they exist) for each discrete time queue length process—the embedded Markov chains, (ii) the stationary distributions  ...  A sufficient condition for w, = EW in GI/D/k to be monotonic in k for a sequence of k-server queues with the same relative traffic intensity is given.  ... 

Page 6910 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
(English summary) Queueing Systems Theory Appl. 20 (1995), no. 1-2, 7-36. The author considers a discrete-time intree network with J queues and multiple classes of customers.  ...  We provide approximations for several different processes, such as the waiting times of successive customers, the remaining workload at an arbitrary time, and the queue length at an arbitrary time, in  ... 

On the throughput, capacity, and stability regions of random multiple access

Jie Luo, A. Ephremides
2006 IEEE Transactions on Information Theory  
Particularly, if a conjectured "sensitivity monotonicity" property held for the stationary distribution of the queues, then equivalence between the closure of the stability region and the throughput region  ...  For a class of packet arrival distributions, we demonstrate that the stationary distribution of the queues possesses positive and strong positive correlation properties, which consequently yield an outer  ...  Thomas Liggett for the insightful discussions on positive correlation and interacting particle systems.  ... 
doi:10.1109/tit.2006.874518 fatcat:ph4ffl23fzhljadxm4p73idlpq

Page 4013 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
) to discrete-time queues.”  ...  Logist. 36 (1989), no. 6, 797-806; MR 91d:60244] studied the priority M/G/1 queue with server vacations and found that the difference between the waiting time distribution under the non-preemptive priority  ... 

Throughput in Processor-Sharing Queues

Na Chen, Scott Jordan
2007 IEEE Transactions on Automatic Control  
While sojourn time is a common performance metric in the queueing literature, average transmission rate is the more commonly discussed metric in the networking literature.  ...  Processor-sharing queues are often used to model file transmission in networks.  ...  In heavy-traffic, Morrison [10] also found the distribution of the response time conditioned on the service time, and Knessl [11] constructed an asymptotic approximation to the sojourn time distribution  ... 
doi:10.1109/tac.2006.887906 fatcat:b4iptblsinejzmudibfob4fudm
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