On the Overflow Process from a Finite Markovian Queue

1984 ◽  
Vol 4 (4) ◽  
pp. 233-240 ◽  
Author(s):  
Erik A. van Doorn
Keyword(s):  
Markovian Queue ◽  
Overflow Process

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.

Time-dependent single server Markovian queue with catastrophe

2015 ◽  
Vol 9 ◽  
pp. 3275-3283
Author(s):  
R. Sudhesh ◽  
A. Vaithiyanathan
Keyword(s):  
Time Dependent ◽  
Single Server ◽  
Markovian Queue

scholarly journals Correlations in Output and Overflow Traffic Processes in Simple Queues

2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Don McNickle
Keyword(s):  
Cross Correlation ◽  
Counting Processes ◽  
Storage Space ◽  
Output Process ◽  
Overflow Traffic ◽  
The Cross ◽  
Departure Processes ◽  
Traffic Processes ◽  
Overflow Process

We consider some simple Markov and Erlang queues with limited storage space. Although the departure processes from some such systems are known to be Poisson, they actually consist of the superposition of two complex correlated processes, the overflow process and the output process. We measure the cross-correlation between the counting processes for these two processes. It turns out that this can be positive, negative, or even zero (without implying independence). The models suggest some general principles on how big these correlations are, and when they are important. This may suggest when renewal or moment approximations to similar processes will be successful, and when they will not.

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