On a certain type of network of queues

1975 ◽  
Vol 12 (1) ◽  
pp. 195-200 ◽  
Author(s):  
K. C. Madan
Keyword(s):  
Steady State ◽  
Single Channel ◽  
Service Channel ◽  
Poisson Stream ◽  
Queue Lengths ◽  
Parallel Channels ◽  
Service Times ◽  
Steady State Probabilities

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S1, S2, …, Sk. After having been serviced at S1, S2, … Sk, the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.

On a certain type of network of queues

1975 ◽  
Vol 12 (01) ◽  
pp. 195-200
Author(s):  
K. C. Madan
Keyword(s):  
Steady State ◽  
Single Channel ◽  
Service Channel ◽  
Poisson Stream ◽  
Queue Lengths ◽  
Parallel Channels ◽  
Service Times ◽  
Steady State Probabilities

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S 1 , S 2, …, Sk. After having been serviced at S 1, S 2, … Sk , the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.

Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

1977 ◽  
Vol 9 (1) ◽  
pp. 141-157 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Explicit Formulas ◽  
State Behavior ◽  
Virtual Waiting Time ◽  
Poisson Arrivals ◽  
Queue Lengths ◽  
The Mean ◽  
Service Times ◽  
Recursive Matrix

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (01) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

1977 ◽  
Vol 9 (01) ◽  
pp. 141-157 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Explicit Formulas ◽  
State Behavior ◽  
Virtual Waiting Time ◽  
Poisson Arrivals ◽  
Queue Lengths ◽  
The Mean ◽  
Service Times ◽  
Recursive Matrix

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (1) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

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