scholarly journals Product-form distributions for an M/G/k group-arrival group-departure loss system

1989 ◽  
Vol 21 (3) ◽  
pp. 721-724 ◽  
Author(s):  
D. Fakinos ◽  
K. Sirakoulis
Keyword(s):  
Equilibrium Distribution ◽  
Product Form ◽  
Loss System ◽  
Group Arrival

In this work we investigate under what circumstances the equilibrium distribution of the numbers of groups of various sizes in a certain M/G/k group-arrival group-departure loss system can be obtained in a closed product form.

scholarly journals Product-form distributions for an M/G/k group-arrival group-departure loss system

1989 ◽  
Vol 21 (03) ◽  
pp. 721-724
Author(s):  
D. Fakinos ◽  
K. Sirakoulis
Keyword(s):  
Equilibrium Distribution ◽  
Product Form ◽  
Loss System ◽  
Group Arrival

In this work we investigate under what circumstances the equilibrium distribution of the numbers of groups of various sizes in a certain M/G/k group-arrival group-departure loss system can be obtained in a closed product form.

The Compensation Approach Applied to a 2 × 2 Switch

1993 ◽  
Vol 7 (4) ◽  
pp. 471-493 ◽  
Author(s):  
O. J. Boxma ◽  
G. J. van Houtum
Keyword(s):  
Generating Functions ◽  
Joint Distribution ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Compensation Approach

In this paper we analyze an asymmetric 2 × 2 buffered switch, fed by two independent Bernoulli input streams. We derive the joint equilibrium distribution of the numbers of messages waiting in the two output buffers. This joint distribution is presented explicitly, without the use of generating functions, in the form of a sum of two alternating series of product-form geometric distributions. The method used is the so-called compensation approach, developed by Adan, Wessels, and Zijm.

Batch Routing Queueing Networks with Jump-Over Blocking

1996 ◽  
Vol 10 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Richard J. Boucherie
Keyword(s):  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Queueing Network ◽  
Capacity Constraints ◽  
Product Form

This paper shows that the equilibrium distribution of a queueing network with batch routing continues to be of product form if a batch that cannot enter its destination — for example, as a consequence of capacity constraints — immediately triggers a new transition that takes up the whole batch.

scholarly journals Discrete-time queueing networks with geometric release probabilities

1992 ◽  
Vol 24 (01) ◽  
pp. 229-233
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Discrete Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Time Interval

This note is concerned with the continuing misconception that a discrete-time network of queues, with independent customer routing and the number of arrivals and services in a time interval following geometric and truncated geometric distributions respectively, has a product-form equilibrium distribution.

scholarly journals Discrete-time queueing networks with geometric release probabilities

1992 ◽  
Vol 24 (1) ◽  
pp. 229-233 ◽  
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Discrete Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Time Interval

This note is concerned with the continuing misconception that a discrete-time network of queues, with independent customer routing and the number of arrivals and services in a time interval following geometric and truncated geometric distributions respectively, has a product-form equilibrium distribution.

The M/G/k group-arrival group-departure loss system

1982 ◽  
Vol 19 (4) ◽  
pp. 826-834 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Poisson Process ◽  
Group Size ◽  
Loss System ◽  
Group Arrival ◽  
Service Times ◽  
Departure Processes

This paper considers the equilibrium behaviour of the M/G/k group-arrival group-departure loss system. Such a system has k servers whose customers arrive in groups, the arrival epochs of groups being points of a Poisson process. The duration of a service can be characteristic of the group size; however, customers who belong to the same group have equal service times. The customers of a group start being served immediately upon their arrival, unless their number is greater than the number of idle servers. In this case the whole group leaves and does not return later (i.e. is lost). Among other things, a generalization of the Erlang B-formula is given and it is shown that the arrival and departure processes are statistically indistinguishable.

Equilibrium results for the M/G/k group-arrival loss system

Top ◽  
2010 ◽  
Vol 21 (1) ◽  
pp. 163-181
Author(s):  
Spiros Dimou ◽  
Demetrios Fakinos
Keyword(s):  
Loss System ◽  
Group Arrival

Some new results on queueing networks with batch movement

1991 ◽  
Vol 28 (02) ◽  
pp. 409-421 ◽  
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Batch Arrivals ◽  
Before And After ◽  
Equilibrium Distributions ◽  
Batch Services ◽  
Independence Results ◽  
Networks Of Queues

Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing. This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained results can be seen as marginal distributions within a more general framework. A generalisation of the classical ‘arrival theorem' for continuous-time networks is given, which compares the equilibrium distribution as seen by arrivals to the time-averaged equilibrium distribution.

scholarly journals PRODUCT-FORM IN G-NETWORKS

2016 ◽  
Vol 30 (3) ◽  
pp. 345-360 ◽  
Author(s):  
Andrea Marin
Keyword(s):  
Stochastic Modeling ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Queueing Network ◽  
Point Of View ◽  
Product Form ◽  
Theoretical Point ◽  
Non Linear ◽  
Modular Analysis ◽  
Product Forms

The introduction of the class of queueing networks called G-networks by Gelenbe has been a breakthrough in the field of stochastic modeling since it has largely expanded the class of models which are analytically or numerically tractable. From a theoretical point of view, the introduction of the G-networks has lead to very important considerations: first, a product-form queueing network may have non-linear traffic equations; secondly, we can have a product-form equilibrium distribution even if the customer routing is defined in such a way that more than two queues can change their states at the same time epoch. In this work, we review some of the classes of product-forms introduced for the analysis of the G-networks with special attention to these two aspects. We propose a methodology that, coherently with the product-form result, allows for a modular analysis of the G-queues to derive the equilibrium distribution of the network.

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