## Algorithm for queueing networks with multi-rate traffic

Publication: Research - peer-review › Journal article – Annual report year: 2011

### Standard

**Algorithm for queueing networks with multi-rate traffic.** / Iversen, Villy Bæk; Ko, King-Tim.

Publication: Research - peer-review › Journal article – Annual report year: 2011

### Harvard

*Advances in Electronics and Telecommunications*, vol 2, no. 3, pp. 3-7.

### APA

*Algorithm for queueing networks with multi-rate traffic*.

*Advances in Electronics and Telecommunications*,

*2*(3), 3-7.

### CBE

### MLA

*Advances in Electronics and Telecommunications*. 2011, 2(3). 3-7.

### Vancouver

### Author

### Bibtex

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### RIS

TY - JOUR

T1 - Algorithm for queueing networks with multi-rate traffic

AU - Iversen,Villy Bæk

AU - Ko,King-Tim

PY - 2011/9

Y1 - 2011/9

N2 - In this paper we present a new algorithm for evaluating queueing networks with multi-rate traffic. The detailed state space of a node is evaluated by explicit formulæ. We consider reversible nodes with multi-rate traffic and find the state probabilities by taking advantage of local balance. Theory of queueing networks in general, presumes that we have product form between the nodes. Otherwise, we have the state space explosion. Even so, the detailed state space of each node may become very large because there is no product form between chains inside a node. A prerequisite for product form is reversibility which implies that the arrival process and departure process are identical processes, for example state-dependent Poisson processes. This property is equivalent to reversibility. Due to product form, an open network with multi-rate traffic is easy to evaluate by convolution algorithms because the nodes behave as independent nodes. For closed queueing networks with multiple servers in every node and multi-rate services we may apply multidimensional convolution algorithm to aggregate the nodes so that we end up with two nodes, the aggregated node and a single node, for which we can calculate the detailed performance measures.

AB - In this paper we present a new algorithm for evaluating queueing networks with multi-rate traffic. The detailed state space of a node is evaluated by explicit formulæ. We consider reversible nodes with multi-rate traffic and find the state probabilities by taking advantage of local balance. Theory of queueing networks in general, presumes that we have product form between the nodes. Otherwise, we have the state space explosion. Even so, the detailed state space of each node may become very large because there is no product form between chains inside a node. A prerequisite for product form is reversibility which implies that the arrival process and departure process are identical processes, for example state-dependent Poisson processes. This property is equivalent to reversibility. Due to product form, an open network with multi-rate traffic is easy to evaluate by convolution algorithms because the nodes behave as independent nodes. For closed queueing networks with multiple servers in every node and multi-rate services we may apply multidimensional convolution algorithm to aggregate the nodes so that we end up with two nodes, the aggregated node and a single node, for which we can calculate the detailed performance measures.

KW - Multi-rate traffic

KW - Reversibility

KW - Convolution algorithm

KW - Product form

KW - Insensitivity

KW - Queueing networks

M3 - Journal article

VL - 2

SP - 3

EP - 7

JO - Advances in Electronics and Telecommunications

T2 - Advances in Electronics and Telecommunications

JF - Advances in Electronics and Telecommunications

SN - 2081-8580

IS - 3

ER -