Queueing analysis of discrete-time buffer systems with compound arrival process and variable service capacity

1995 ◽  
pp. 41-55
Author(s):  
Bart Vinck ◽  
Herwig Bruneel
Keyword(s):  
Discrete Time ◽  
Arrival Process ◽  
Queueing Analysis ◽  
Service Capacity ◽  
Time Buffer

scholarly journals Discrete-time buffer systems with session-based arrival streams

2010 ◽  
Vol 67 (6) ◽  
pp. 432-450 ◽  
Author(s):  
L. Hoflack ◽  
S. De Vuyst ◽  
S. Wittevrongel ◽  
H. Bruneel
Keyword(s):  
Discrete Time ◽  
Time Buffer

scholarly journals Recursive filters for partially observable finite Markov chains

2005 ◽  
Vol 42 (03) ◽  
pp. 684-697 ◽  
Author(s):  
James Ledoux
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Arrival Process ◽  
Estimation Of Parameters ◽  
Batch Markovian Arrival Process ◽  
Recursive Filters ◽  
Conditional Expectations ◽  
Finite Markov Chains ◽  
Partially Observable ◽  
Recursive Equations

In this note, we consider discrete-time finite Markov chains and assume that they are only partly observed. We obtain finite-dimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving conditional expectations. An application to the estimation of parameters of the so-called discrete-time batch Markovian arrival process is outlined.

scholarly journals A queue with semiperiodic traffic

2005 ◽  
Vol 37 (1) ◽  
pp. 160-184 ◽  
Author(s):  
Juan Alvarez ◽  
Bruce Hajek
Keyword(s):  
Discrete Time ◽  
Length Distribution ◽  
Arrival Rate ◽  
Arrival Process ◽  
Service Rate ◽  
Diffusion Limit ◽  
Time Analysis ◽  
Queueing Process ◽  
Brownian Bridges ◽  
Overflow Probability

In this paper, we analyze the diffusion limit of a discrete-time queueing system with constant service rate and connections that randomly enter and depart from the system. Each connection generates periodic traffic while it is active, and a connection's lifetime has finite mean. This can model a time division multiple access system with constant bit-rate connections. The diffusion scaling retains semiperiodic behavior in the limit, allowing for both short-time analysis (within one frame) and long-time analysis (over multiple frames). Weak convergence of the cumulative arrival process and the stationary buffer-length distribution is proved. It is shown that the limit of the cumulative arrival process can be viewed as a discrete-time stationary-increment Gaussian process interpolated by Brownian bridges. We present bounds on the overflow probability of the limit queueing process as functions of the arrival rate and the connection lifetime distribution. Also, numerical and simulation results are presented for geometrically distributed connection lifetimes.

scholarly journals Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-$MAP/G_n^{(a,b)}/1$

2021 ◽  
Author(s):  
Umesh Chandra Gupta ◽  
Nitin Kumar ◽  
Sourav Pradhan ◽  
Farida Parvez Barbhuiya ◽  
Mohan L Chaudhry
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Service Time ◽  
Batch Size ◽  
Arrival Process ◽  
General Distribution ◽  
Complete Analysis ◽  
Service Rate ◽  
Single Server ◽  
Digital Platforms

Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epochs, where the first is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by some numerical examples.

scholarly journals Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yung-Chung Wang ◽  
Dong-Liang Cai ◽  
Li-Hsin Chiang ◽  
Cheng-Wei Hu
Keyword(s):  
Discrete Time ◽  
Packet Loss ◽  
Loss Probability ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Service Process ◽  
Batch Service ◽  
Temporal Behavior ◽  
Packet Loss Probability ◽  
Batch Markovian Arrival Process

This paper applies a matrix-analytical approach to analyze the temporal behavior of Markovian-modulated batch-service queue with discrete-time batch Markovian arrival process (DBMAP). The service process is correlated and its structure is presented through discrete-time batch Markovian service process (DBMSP). We examine the temporal behavior of packet loss by means of conditional statistics with respect to congested and noncongested periods that occur in an alternating manner. The congested period corresponds to having more than a certain number of packets in the buffer; noncongested period corresponds to the opposite. All of the four related performance measures are derived, including probability distributions of a congested and noncongested periods, the probability that the system stays in a congested period, the packet loss probability during congested period, and the long term packet loss probability. Queueing systems of this type arise in the domain of wireless communications.

scholarly journals Discrete-time queues with variable service capacity: a basic model and its analysis

2013 ◽  
Vol 239 (2) ◽  
pp. 359-380 ◽  
Author(s):  
Herwig Bruneel ◽  
Sabine Wittevrongel ◽  
Dieter Claeys ◽  
Joris Walraevens
Keyword(s):  
Discrete Time ◽  
Service Capacity ◽  
Its Analysis ◽  
Basic Model ◽  
Discrete Time Queues ◽  
Time Queues
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