Overland flow as a queueing process: The B/D/1 queue with an arbitrary service time

2016 ◽  
Vol 106 ◽  
pp. 19-29 ◽  
Author(s):  
Emmanuel Mouche ◽  
Marie-Alice Harel
Keyword(s):  
Service Time ◽  
Overland Flow ◽  
Queueing Process ◽  
Arbitrary Service Time

On queueing systems by retrials

1983 ◽  
Vol 20 (02) ◽  
pp. 380-389 ◽  
Author(s):  
Vidyadhar G. Kulkarni
Keyword(s):  
General Result ◽  
Service Time ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Waiting Room ◽  
Second Moments ◽  
Different Types ◽  
General Distributions ◽  
Arbitrary Service Time

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.

An extension of Erlang's formulas which distinguishes individual servers

1972 ◽  
Vol 9 (1) ◽  
pp. 192-197 ◽  
Author(s):  
Jan M. Chaiken ◽  
Edward Ignall
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
The State ◽  
Service Time Distribution ◽  
Loss System ◽  
Arbitrary Service Time

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.

On queueing systems by retrials

1983 ◽  
Vol 20 (2) ◽  
pp. 380-389 ◽  
Author(s):  
Vidyadhar G. Kulkarni
Keyword(s):  
General Result ◽  
Service Time ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Waiting Room ◽  
Second Moments ◽  
Different Types ◽  
General Distributions ◽  
Arbitrary Service Time

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.

An extension of Erlang's formulas which distinguishes individual servers

1972 ◽  
Vol 9 (01) ◽  
pp. 192-197 ◽  
Author(s):  
Jan M. Chaiken ◽  
Edward Ignall
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
The State ◽  
Service Time Distribution ◽  
Loss System ◽  
Arbitrary Service Time

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.

scholarly journals A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time

1992 ◽  
Vol 15 (1) ◽  
pp. 189-194 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Lotfi Tadj
Keyword(s):  
Explicit Formula ◽  
Stationary Distribution ◽  
Service Time ◽  
Random Number ◽  
Queueing System ◽  
Time Dependent ◽  
Batch Size ◽  
Single Server ◽  
Variable Size ◽  
Queueing Process

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at leastrthe server takes a batch of sizerand processes it a random time arbitrarily distributed. If the queueing level is less thanrthe server idles until the queue accumulatesrcustomers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.The objective of the paper is the stationary distribution of queueing process which is studied via semi-regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.

Algebraic Solution of the Horton-Izzard Turbulent Overland Flow Model of the Rising Hydrograph

1977 ◽  
Vol 8 (4) ◽  
pp. 249-256 ◽  
Author(s):  
Mohammad Akram Gill
Keyword(s):  
Differential Equation ◽  
Turbulent Flow ◽  
Flow Model ◽  
Overland Flow ◽  
Flow Equation ◽  
Algebraic Solution ◽  
Mixed Flow ◽  
Overland Flow Model

In the differential equation of the overland turbulent flow which was first postulated by Horton, Eq.(6), the value of c equals 5/3. For this value of c, the flow equation could not be integrated algebraically. Horton solved the equation for c = 2 and believed that his solution was valid for mixed flow. The flow equation with c = 5/3 is solved algebraically herein. It is shown elsewhere (Gill 1976) that the flow equation can indeed be integrated for any rational value of c.

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