Networks of queues with customers of different types

1975 ◽  
Vol 12 (03) ◽  
pp. 542-554 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Service Time Distribution ◽  
Basic Model ◽  
Open Case ◽  
Negative Exponential Distribution ◽  
Different Types ◽  
The Individual ◽  
Negative Exponential ◽  
Networks Of Queues

The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution. Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.

Networks of queues with customers of different types

1975 ◽  
Vol 12 (3) ◽  
pp. 542-554 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Service Time Distribution ◽  
Basic Model ◽  
Open Case ◽  
Negative Exponential Distribution ◽  
Different Types ◽  
The Individual ◽  
Negative Exponential ◽  
Networks Of Queues

The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution.Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.

A Note on Queueing Networks with Signals and Random Triggering Times

1994 ◽  
Vol 8 (2) ◽  
pp. 213-219 ◽  
Author(s):  
Xiuli Chao
Keyword(s):  
Stationary Distribution ◽  
Service Time ◽  
Queueing Networks ◽  
Time Distribution ◽  
Network Models ◽  
Form Solution ◽  
Service Time Distribution ◽  
Signal Changes ◽  
Networks Of Queues ◽  
Random Amount

There is a growing interest in networks of queues with customers and signals. The signals in these models carry commands to the service nodes and trigger customers to move instantaneously within the network. In this note we consider networks of queues with signals and random triggering times; that is, when a signal arrives at a node, it takes a random amount of time to trigger a customer to move with distribution depending on the source of the signal. By appropriately choosing the triggering times, we can obtain network models such that a signal changes a customer's service time distribution – for example, the signal increases or decreases the service time of a customer. We show that the stationary distribution of this model has a product form solution.

scholarly journals Imbedded Markov chain analysis of single server bulk queues

1964 ◽  
Vol 4 (2) ◽  
pp. 244-263 ◽  
Author(s):  
U. Narayan Bhat
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Arrival Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Chain Analysis ◽  
Special Cases ◽  
Poisson Arrivals ◽  
Negative Exponential

SummaryIn this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.

Hitting time in an M/G/1 queue

1999 ◽  
Vol 36 (03) ◽  
pp. 934-940 ◽  
Author(s):  
Sheldon M. Ross ◽  
Sridhar Seshadri
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Arrival Rate ◽  
Hitting Time ◽  
Service Time Distribution ◽  
Expected Time ◽  
Efficient Simulation ◽  
Simulation Procedure ◽  
Poisson Arrival ◽  
Stationary Delay

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

The general bulk queue as a matrix factorisation problem of the Wiener-Hopf type. Part II.

1975 ◽  
Vol 7 (3) ◽  
pp. 647-655 ◽  
Author(s):  
John Dagsvik
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Time Process ◽  
Waiting Time Process ◽  
Bulk Queue ◽  
Erlang Distributions ◽  
Matrix Factorisation

In a previous paper (Dagsvik (1975)) the waiting time process of the single server bulk queue is considered and a corresponding waiting time equation is established. In this paper the waiting time equation is solved when the inter-arrival or service time distribution is a linear combination of Erlang distributions. The analysis is essentially based on algebraic arguments.

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.

scholarly journals s,S Inventory with Positive Service Time and Retrial of Demands: An Approach through Multiserver Queues

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Anoop N. Nair ◽  
M. J. Jacob
Keyword(s):  
Steady State ◽  
Poisson Process ◽  
Service Time ◽  
Time Distribution ◽  
Joint Distribution ◽  
Service Time Distribution ◽  
Exponential Rate ◽  
Numerical Illustration ◽  
Multiserver Queues ◽  
Geometric Methods

We analyze an s,S inventory with positive service time and retrial of demands by considering the inventory as servers of a multiserver queuing system. Demands arrive according to a Poisson process and service time distribution is exponential. On each service completion, the number of demands in the system as well as the number of inventories (servers) is reduced by one. When all servers are busy, new arrivals join an orbit from which they try to access the service at an exponential rate. Using matrix geometric methods the steady state joint distribution of the demands and inventory has been analyzed and a numerical illustration is given.

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