Exponential Interarrival and Service Times: Closed-Form Expressions

2012 ◽  
pp. 69-116
Keyword(s):  
Closed Form ◽  
Service Times

scholarly journals Tails in generalized Jackson networks with subexponential service-time distributions

2005 ◽  
Vol 42 (2) ◽  
pp. 513-530 ◽  
Author(s):  
François Baccelli ◽  
Serguei Foss ◽  
Marc Lelarge
Keyword(s):  
Closed Form ◽  
Service Time ◽  
Large Deviation ◽  
Exact Asymptotics ◽  
Fluid Limits ◽  
Jackson Networks ◽  
Single Station ◽  
Service Times

We give the exact asymptotics of the tail of the stationary maximal dater in generalized Jackson networks with subexponential service times. This maximal dater, which is an analogue of the workload in an isolated queue, gives the time taken to clear all customers present at some time t when stopping all arrivals that take place later than t. We use the property that a large deviation of the maximal dater is caused by a single large service time at a single station at some time in the distant past of t, in conjunction with fluid limits of generalized Jackson networks, to derive the relevant asymptotics in closed form.

On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

2007 ◽  
Vol 44 (02) ◽  
pp. 379-392
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Closed Form ◽  
Long Range ◽  
Covariance Function ◽  
Queueing System ◽  
Regenerative Process ◽  
Long Range Dependence ◽  
Exact Asymptotics ◽  
Regenerative Processes ◽  
Service Times ◽  
Heavy Tailed

In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

scholarly journals On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

2007 ◽  
Vol 44 (02) ◽  
pp. 379-392
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Closed Form ◽  
Long Range ◽  
Covariance Function ◽  
Queueing System ◽  
Regenerative Process ◽  
Long Range Dependence ◽  
Exact Asymptotics ◽  
Regenerative Processes ◽  
Service Times ◽  
Heavy Tailed

In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

scholarly journals Tails in generalized Jackson networks with subexponential service-time distributions

2005 ◽  
Vol 42 (02) ◽  
pp. 513-530 ◽  
Author(s):  
François Baccelli ◽  
Serguei Foss ◽  
Marc Lelarge
Keyword(s):  
Closed Form ◽  
Service Time ◽  
Large Deviation ◽  
Exact Asymptotics ◽  
Fluid Limits ◽  
Jackson Networks ◽  
Single Station ◽  
Service Times

We give the exact asymptotics of the tail of the stationary maximal dater in generalized Jackson networks with subexponential service times. This maximal dater, which is an analogue of the workload in an isolated queue, gives the time taken to clear all customers present at some time t when stopping all arrivals that take place later than t. We use the property that a large deviation of the maximal dater is caused by a single large service time at a single station at some time in the distant past of t, in conjunction with fluid limits of generalized Jackson networks, to derive the relevant asymptotics in closed form.

scholarly journals On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

2007 ◽  
Vol 44 (2) ◽  
pp. 379-392 ◽  
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Closed Form ◽  
Long Range ◽  
Covariance Function ◽  
Queueing System ◽  
Regenerative Process ◽  
Long Range Dependence ◽  
Exact Asymptotics ◽  
Regenerative Processes ◽  
Service Times ◽  
Heavy Tailed

In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

scholarly journals On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Rehab F. Khalaf ◽  
Kailash C. Madan ◽  
Cormac A. Lukas
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Waiting Time ◽  
Generating Functions ◽  
Queuing System ◽  
Sudden Failure ◽  
Supplementary Variables ◽  
Service Times ◽  
Mathcad Software ◽  
Number Of Customers

We study a queuing system which is equipped with a stand-by server in addition to the main server. The stand-by server provides service to customers only during the period of absence of the main server when either the main server is on a vacation or it is in the state of repairs due to a sudden failure from time to time. The service times, vacation times, and repair times are assumed to follow general arbitrary distributions while the stand-by service times follow exponential distribution. Supplementary variables technique has been used to obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue while the MathCad software has been used to illustrate the numerical results in this work.

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