Buffer overflow asymptotics for a buffer handling many traffic sources

1996 ◽  
Vol 33 (03) ◽  
pp. 886-903 ◽  
Author(s):  
Costas Courcoubetis ◽  
Richard Weber
Keyword(s):  
Generating Functions ◽  
Optimization Problem ◽  
Buffer Overflow ◽  
Buffer Size ◽  
Arrival Process ◽  
Service Rate ◽  
Atm Switch ◽  
Constant Rate ◽  
Source Models ◽  
Markov Modulated

As a model for an ATM switch we consider the overflow frequency of a queue that is served at a constant rate and in which the arrival process is the superposition of N traffic streams. We consider an asymptotic as N → ∞ in which the service rate Nc and buffer size Nb also increase linearly in N. In this regime, the frequency of buffer overflow is approximately exp(–NI(c, b)), where I(c, b) is given by the solution to an optimization problem posed in terms of time-dependent logarithmic moment generating functions. Experimental results for Gaussian and Markov modulated fluid source models show that this asymptotic provides a better estimate of the frequency of buffer overflow than ones based on large buffer asymptotics.

Buffer overflow asymptotics for a buffer handling many traffic sources

1996 ◽  
Vol 33 (3) ◽  
pp. 886-903 ◽  
Author(s):  
Costas Courcoubetis ◽  
Richard Weber
Keyword(s):  
Generating Functions ◽  
Optimization Problem ◽  
Buffer Overflow ◽  
Buffer Size ◽  
Arrival Process ◽  
Service Rate ◽  
Atm Switch ◽  
Constant Rate ◽  
Source Models ◽  
Markov Modulated

As a model for an ATM switch we consider the overflow frequency of a queue that is served at a constant rate and in which the arrival process is the superposition of N traffic streams. We consider an asymptotic as N → ∞ in which the service rate Nc and buffer size Nb also increase linearly in N. In this regime, the frequency of buffer overflow is approximately exp(–NI(c, b)), where I(c, b) is given by the solution to an optimization problem posed in terms of time-dependent logarithmic moment generating functions. Experimental results for Gaussian and Markov modulated fluid source models show that this asymptotic provides a better estimate of the frequency of buffer overflow than ones based on large buffer asymptotics.

A Convexity Property of a Markov-Modulated Queueing Loss System

1995 ◽  
Vol 9 (2) ◽  
pp. 193-199 ◽  
Author(s):  
Charles Du ◽  
Michael Pinedo
Keyword(s):  
Transition Probability ◽  
Loss Probability ◽  
Arrival Process ◽  
Service Rate ◽  
Single Server ◽  
Convexity Property ◽  
Loss System ◽  
Markov Modulated Poisson Process ◽  
Speed Parameter ◽  
Markov Modulated

In this note we consider a single-server queueing loss system with zero buffer. The arrival process is a nonstationary Markov-modulated Poisson process. The arrival process in state i is Poisson with rate λi. The process remains in state i for a time that is exponentially distributed with rate Cαi, with c being a control or speed parameter. The service rate in state i is exponentially distributed with rate μi. The process moves from state i to state j with transition probability qij. We are interested in the loss probability as a function of c. In this note we show that, under certain conditions, the loss probability decreases when the c increases. As such, this result generalizes a result obtained earlier by Fond and Ross.

scholarly journals Performance Measures of State Dependent MMPP/M/1 Queue

2018 ◽  
Vol 7 (4.10) ◽  
pp. 942 ◽  
Author(s):  
R. Sakthi ◽  
V. Vidhya ◽  
K. Mahaboob Hassain Sherieff ◽  
. .
Keyword(s):  
Performance Measures ◽  
Research Work ◽  
Arrival Process ◽  
Service Rate ◽  
Single Server ◽  
State Dependent ◽  
Markov Modulated ◽  
Service State ◽  
Modulated Process ◽  
Stationary Probability Vector

In this research work we are concerned with single unit server queue  queue with Markov Modulated process in Poisson fashion and the service time follow exponential distribution. The system is framed as a state dependent with the arrival process as Markov Modulated input and service is rendered by a single server with variation in service rate based on the intensity of service state of the system. The rate matrix that is essential to compute the stationary probability vector is obtained and various performance measures are computed using matrix method.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

Analysis of separable Markov-modulated rate models for information-handling systems

1991 ◽  
Vol 23 (01) ◽  
pp. 105-139 ◽  
Author(s):  
Thomas E. Stern ◽  
Anwar I. Elwalid
Keyword(s):  
Solution Technique ◽  
Service Rate ◽  
Processing Unit ◽  
Equilibrium Equations ◽  
Flow Models ◽  
Separability Property ◽  
Finite State ◽  
Service Rates ◽  
Rate Processes ◽  
Markov Modulated

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

Modeling and Simulation of Self-Similar Traffic in Wireless IP Networks

2011 ◽  
pp. 249-265
Author(s):  
Dimitar Radev ◽  
Izabella Lokshina ◽  
Svetla Radeva
Keyword(s):  
Network Traffic ◽  
Traffic Load ◽  
Single Server ◽  
Finite Buffer ◽  
Wide Range ◽  
Telecommunications Network ◽  
Source Models ◽  
Wireless Ip ◽  
Self Similar ◽  
Markov Modulated

The paper examines self-similar properties of real telecommunications network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Simulation with stochastic and long range dependent traffic source models is performed, and the algorithms for buffer overflow simulation for finite buffer single server model under self-similar traffic load SSM/M/1/B are explained. The algorithms for modeling fixed-length sequence generators that are used to simulate self-similar behavior of wireless IP network traffic are developed and applied. Numerical examples are provided, and simulation results are analyzed.

A MULTI-SERVER QUEUEING MODEL WITH MARKOVIAN ARRIVALS AND MULTIPLE THRESHOLDS

2007 ◽  
Vol 24 (02) ◽  
pp. 223-243 ◽  
Author(s):  
SRINIVAS R. CHAKRAVARTHY
Keyword(s):  
Optimization Problem ◽  
Arrival Process ◽  
Single Server ◽  
Queueing Model ◽  
Process Map ◽  
Practical Applications ◽  
Setup Costs ◽  
Multiple Thresholds ◽  
Minimum Delay ◽  
Multi Server

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classical MAP/M/c queueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classical MAP/M/c model.

Analysis of separable Markov-modulated rate models for information-handling systems

1991 ◽  
Vol 23 (1) ◽  
pp. 105-139 ◽  
Author(s):  
Thomas E. Stern ◽  
Anwar I. Elwalid
Keyword(s):  
Solution Technique ◽  
Service Rate ◽  
Processing Unit ◽  
Equilibrium Equations ◽  
Flow Models ◽  
Separability Property ◽  
Finite State ◽  
Service Rates ◽  
Rate Processes ◽  
Markov Modulated

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP).In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

Analysis of a Discrete-Time Queueing System with a Markov-Modulated input Process and constant service Rate

1996 ◽  
Vol 10 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Woo-Yong Choi ◽  
Chi-Hyuck Jun
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Service Rate ◽  
System State ◽  
Input Process ◽  
New Approach ◽  
One Dimensional ◽  
Markov Modulated ◽  
Modulated Process ◽  
Renewal Cycle

We propose a new approach to the analysis of a discrete-time queueing system whose input is generated by a Markov-modulated process and whose service rate is constant. Renewal cycles are identified and the system state on each renewal cycle is modeled as a one-dimensional Markov chain.

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