In this paper, the authors consider a concentrating tree queuing network with an arbitrary number of nodes. Packets of fixed size 1 arrive from the exterior of the network to each node, where they are queued. After being served they are transmitted downstream to the next node in their crossing path through the different levels of the network. In this model each node, except node 0, is a single server polling system with an arbitrary and unspecified number of queues. All packets leave the network via the same node, the sink, which is called node 0. Node 0 is a single server polling system with N queues. Each queue i, for i = 1,...,N in node 0, may store packets arriving from the corresponding node i upstream in the network or directly from the exterior. Packets that pass through queue i of node 0 are classified as ‘type i’ packets, for i = 1,...,N. The network operates in discrete time and packets arrive from the exterior, in batches at slot boundaries, according to independent Bernoulli arrival processes. Except for node 0, the service disciplines are arbitrary. The service discipline of node 0 must be HoL-based. This means that the server allocation policy to queues in the node may only depend on whether or not queues are occupied and not on the number of packets present in each queue. For the queuing network system defined above, the authors construct a system consisting of only one node with N queues, called the reduced system. The reduced system uses the same service discipline as node 0 in the main network and its arrival processes are given by superposition of the arrivals to nodes upstream of node i, for i = 1,...,N. In this context the authors establish a relation in distribution between the contents of the main network and the reduced system. They show that the mean end-to-end delays of type i packets in the main network and the reduced system are equal. Leonardo Pasini

Recensione dell'articolo: (Beekhuizen, Paul; Denteneer, Dee; Resing, Jacques - " Reduction of a polling network to a single node " - Queueing Syst. 58 (2008), no.4, 303–319.)

PASINI, Leonardo
2009-01-01

Abstract

In this paper, the authors consider a concentrating tree queuing network with an arbitrary number of nodes. Packets of fixed size 1 arrive from the exterior of the network to each node, where they are queued. After being served they are transmitted downstream to the next node in their crossing path through the different levels of the network. In this model each node, except node 0, is a single server polling system with an arbitrary and unspecified number of queues. All packets leave the network via the same node, the sink, which is called node 0. Node 0 is a single server polling system with N queues. Each queue i, for i = 1,...,N in node 0, may store packets arriving from the corresponding node i upstream in the network or directly from the exterior. Packets that pass through queue i of node 0 are classified as ‘type i’ packets, for i = 1,...,N. The network operates in discrete time and packets arrive from the exterior, in batches at slot boundaries, according to independent Bernoulli arrival processes. Except for node 0, the service disciplines are arbitrary. The service discipline of node 0 must be HoL-based. This means that the server allocation policy to queues in the node may only depend on whether or not queues are occupied and not on the number of packets present in each queue. For the queuing network system defined above, the authors construct a system consisting of only one node with N queues, called the reduced system. The reduced system uses the same service discipline as node 0 in the main network and its arrival processes are given by superposition of the arrivals to nodes upstream of node i, for i = 1,...,N. In this context the authors establish a relation in distribution between the contents of the main network and the reduced system. They show that the mean end-to-end delays of type i packets in the main network and the reduced system are equal. Leonardo Pasini
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/333183
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