An empirical study on TCP flow interarrival time distribution for normal and anomalous traffic

2014 ◽  
Vol 30 (1) ◽  
pp. e2881 ◽  
Author(s):  
Laleh Arshadi ◽  
Amir Hossein Jahangir
Keyword(s):  
Empirical Study ◽  
Time Distribution ◽  
Interarrival Time

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

scholarly journals Processor-sharing and random-service queues with semi-Markovian arrivals

2005 ◽  
Vol 42 (02) ◽  
pp. 478-490
Author(s):  
De-An Wu ◽  
Hideaki Takagi
Keyword(s):  
Waiting Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Interarrival Time ◽  
Size Distributions ◽  
Processor Sharing ◽  
Queue Size ◽  
Mean Waiting Time ◽  
The Mean

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-lcustomer who, upon his arrival, meetskcustomers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-lcustomer who, upon his arrival, meetsk+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (1) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated.The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

scholarly journals A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution

1998 ◽  
Vol 11 (3) ◽  
pp. 247-254 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Asymptotic Series ◽  
Traffic Load ◽  
Interarrival Time ◽  
Service Time Distribution ◽  
Tail Probabilities ◽  
S Transform ◽  
Stationary Waiting Time

For the GI/G/1 queueing model with traffic load a<1, service time distribution B(t) and interarrival time distribution A(t), whenever for t→∞1−B(t)∼c(t/β)ν+O(e−δt),c>0,1<ν<2,δ>0, and ∫0∞tμdA(t)<∞ for μ>ν, (1−a)1ν−1w converges in distribution for a↑1. Here w is distributed as the stationary waiting time distribution. The L.-S. transform of the limiting distribution is derived and an asymptotic series for its tail probabilities is obtained. The theorem actually proved in the text concerns a slightly more general asymptotic behavior of 1−B(t), t→∞, than mentioned above.

On renewal processes relating to counter models: the case of phase-type interarrival times

1993 ◽  
Vol 30 (1) ◽  
pp. 175-183 ◽  
Author(s):  
Edward P. C. Kao ◽  
Marion Spokony Smith
Keyword(s):  
Time Distribution ◽  
Interarrival Time ◽  
Applied Probability ◽  
Renewal Processes ◽  
Type I ◽  
Type Ii ◽  
Inventory Models ◽  
Phase Type ◽  
Interarrival Times

The Type I and Type II counter models of Pyke (1958) have many applications in applied probability: in reliability, queueing and inventory models, for example. In this paper, we study the case in which the interarrival time distribution is of phase type. For the two counter models, we derive the renewal functions of the related renewal processes and propose approaches for their computations.

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