Paul Beekhuizen

Performance analysis of small non-uniform packet switches

Packet switches have been studied extensively as part of ATM and LAN networks under the assumption that the number of input ports N tends to infinity. Our study of packet switches is motivated by networks on chips, where N is usually 4 or 5 and asymptotic models lead to inaccurate results. We consider small non-uniform switches and accurately approximate stability conditions and throughput. In addition to this, we approximate the mean waiting time in the switch by that in a ./Geo/1 queue.

Analysis of a tandem network model of a single-router Network-on-Chip

We study a single-router Network-on-Chip modelled as a tandem queueing network. The first node is a geoK/D/1 queue (K fixed) representing a network interface, and the second node is a ./G/1 queue representing the packet switch. If K>1 we have train arrivals at the second node. If K=1 the arrival process of the second node reduces to a Bernoulli process. In the latter case, routers have been studied extensively as part of ATM and LAN networks under the assumption that the number of input ports N tends to infinity. In Networks-on-Chips N is usually 4 or 5 and results for ATM and LAN routers lead to inaccurate results. We introduce a new approximation scheme that yields accurate results for small switches. In addition to this we analyse the tandem network, both for K=1 and K>1, and we approximate the mean sojourn time in the switch and the mean end-to-end delay. If N=4 our approximation has a relative error of only 4.5% if K=6 and 1% if K=1.

An Analytical Study of Network Coding in the Presence of Real-Time Messages

With network coding, two data packets are transformed into one by a simple XOR-operation. The transformed packet is transmitted and each original packet can be retrieved at its destination node through a similar XOR-operation. Network coding is an important research topic as it radically challenges existing networking paradigms. In this paper we provide an analytical study of the impact network coding has on the delivery of real-time packets (i.e., packets with deadlines). We model a router as a queueing system where packets arrive from two independent Poisson flows. We obtain an exact expression for the goodput of the system and study the goodput gain that can be achieved by performing network coding. We verify the validity of the model through simulations.

Packet skipping and network coding for delay-sensitive network communication

We provide an analytical study of the impact of packet skipping and opportunistic network coding on the timely communication of messages through a single network element. In a first step, we consider a single-server queueing system with Poisson arrivals, exponential service times, and a single buffer position. Packets arriving at a network node have a fixed deadline before which they should reach the destination. To preserve server capacity, we introduce a thresholding policy, based on remaining time until deadline expiration, to decide whether to serve a packet or skip its service. The obtained goodput improvement of the system is derived, as well as the operating conditions under which thresholding can enhance the performance. Subsequently, we focus our analysis on a system that supports network coding instead of thresholding. We characterize the impact of network coding at a router node on the delivery of packets associated with deadlines. We model the router node as a queueing system in which packets arrive from two independent Poisson flows and undergo opportunistic coding operations. We obtain an exact expression for the goodput of the system and study the achievable gain. Finally, we provide an analytical model that considers both network coding and packet skipping, capturing their joint performance. A comparative analysis between the aforementioned approaches is provided.