Conditional job-observer property for multitype closed queueing networks

2002 ◽  
Vol 39 (04) ◽  
pp. 865-881 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Cycle Time ◽  
Queueing Networks ◽  
Closed Queueing Networks ◽  
Basic Formula ◽  
Sojourn Times ◽  
Number Of Customers ◽  
Insight Into

For functionals of multitype closed queueing networks, a conditional job-observer property is shown which provides more insight into the classical job-observer property. Applications and examples are given, including the classical job-observer property for the number of customers in a network, a representation of cycle time distributions and a basic formula for sojourn times.

Conditional job-observer property for multitype closed queueing networks

2002 ◽  
Vol 39 (4) ◽  
pp. 865-881 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Cycle Time ◽  
Queueing Networks ◽  
Closed Queueing Networks ◽  
Basic Formula ◽  
Sojourn Times ◽  
Number Of Customers ◽  
Insight Into

For functionals of multitype closed queueing networks, a conditional job-observer property is shown which provides more insight into the classical job-observer property. Applications and examples are given, including the classical job-observer property for the number of customers in a network, a representation of cycle time distributions and a basic formula for sojourn times.

scholarly journals Analysis of Closed Queueing Networks with Batch Service

2020 ◽  
Vol 20 (4) ◽  
pp. 527-533
Author(s):  
Elena P. Stankevich ◽  
◽  
Igor E. Tananko ◽  
Vitalii I. Dolgov ◽  
◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Queueing Network ◽  
Transport Systems ◽  
Batch Service ◽  
Single Server ◽  
Closed Queueing Networks ◽  
Number Of Customers

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

On normalization constants for closed queueing networks with finite local buffers

1998 ◽  
Vol 35 (3) ◽  
pp. 600-607
Author(s):  
Ulrich A. W. Tetzlaff
Keyword(s):  
Queueing Networks ◽  
Delta Function ◽  
Partition Functions ◽  
Balance Equations ◽  
Steady State Flow ◽  
Closed Queueing Networks ◽  
Single Class ◽  
Closed Form Solutions ◽  
Flow Balance ◽  
Number Of Customers

We present new closed form solutions for partition functions used to normalize the steady-state flow balance equations of certain Markovian type queueing networks. The results focus on single class closed product form networks with state space constraints at the queueing stations. They are achieved by combining the partition function of the open network, having finite local buffers with a delta function in order to fix the number of customers in the system.

Conditional expected sojourn times in insensitive queueing systems and networks

1984 ◽  
Vol 16 (4) ◽  
pp. 906-919 ◽  
Author(s):  
Uwe Jansen
Keyword(s):  
Queueing Networks ◽  
Point Processes ◽  
Response Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Main Tool ◽  
Closed Queueing Networks ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Special Cases

We consider queueing systems where the stationary state probabilities are insensitive with respect to the distribution of certain basic random variables such as service requirements, interarrival times, repair times, etc. The conditional expected sojourn times are stated as Radon–Nikodym densities of the stationary distribution at jump points of the queueing system. The conditions are the given values of such basic random variables for which the insensitivity is valid. We use stationary point processes as our main tool. This means that dependences between certain basic random variables are permitted. Conditional expected real service times, conditional mean response times in closed queueing networks, and similar conditional expected values, are dealt with as special cases.

On normalization constants for closed queueing networks with finite local buffers

1998 ◽  
Vol 35 (03) ◽  
pp. 600-607
Author(s):  
Ulrich A. W. Tetzlaff
Keyword(s):  
Queueing Networks ◽  
Delta Function ◽  
Partition Functions ◽  
Balance Equations ◽  
Steady State Flow ◽  
Closed Queueing Networks ◽  
Single Class ◽  
Closed Form Solutions ◽  
Flow Balance ◽  
Number Of Customers

We present new closed form solutions for partition functions used to normalize the steady-state flow balance equations of certain Markovian type queueing networks. The results focus on single class closed product form networks with state space constraints at the queueing stations. They are achieved by combining the partition function of the open network, having finite local buffers with a delta function in order to fix the number of customers in the system.

Sojourn times in closed queueing networks

1983 ◽  
Vol 15 (03) ◽  
pp. 638-656 ◽  
Author(s):  
F. P. Kelly ◽  
P. K. Pollett
Keyword(s):  
Free Path ◽  
Queueing Networks ◽  
Joint Distribution ◽  
The State ◽  
Product Form ◽  
Closed Queueing Networks ◽  
Jackson Network ◽  
Simple Representation ◽  
Sojourn Times

This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.

Conditional expected sojourn times in insensitive queueing systems and networks

1984 ◽  
Vol 16 (04) ◽  
pp. 906-919 ◽  
Author(s):  
Uwe Jansen
Keyword(s):  
Queueing Networks ◽  
Point Processes ◽  
Response Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Main Tool ◽  
Closed Queueing Networks ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Special Cases

We consider queueing systems where the stationary state probabilities are insensitive with respect to the distribution of certain basic random variables such as service requirements, interarrival times, repair times, etc. The conditional expected sojourn times are stated as Radon–Nikodym densities of the stationary distribution at jump points of the queueing system. The conditions are the given values of such basic random variables for which the insensitivity is valid. We use stationary point processes as our main tool. This means that dependences between certain basic random variables are permitted. Conditional expected real service times, conditional mean response times in closed queueing networks, and similar conditional expected values, are dealt with as special cases.

Sojourn times in closed queueing networks

1983 ◽  
Vol 15 (3) ◽  
pp. 638-656 ◽  
Author(s):  
F. P. Kelly ◽  
P. K. Pollett
Keyword(s):  
Free Path ◽  
Queueing Networks ◽  
Joint Distribution ◽  
The State ◽  
Product Form ◽  
Closed Queueing Networks ◽  
Jackson Network ◽  
Simple Representation ◽  
Sojourn Times

This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.

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