MODELS OF CONCURRENT ARCHITECTURES - Modelling with Generalised Stochastic Petri Nets - page 248

Figure 11.1: Regular mesh of processing elements
each processor is directly connected to its local neighbours. GSPN models
for this class of architectures are developed under the assumptions that the
workload is evenly distributed across all the processing elements and the
computations assigned to each processor entail interactions with the local
neighbours only (thus, we neglect any routing problem).
The first step of the modelling procedure is the development of basic GSPN
models of the behaviour of a single processing unit. Models for multipro-
cessor architectures will be obtained combining, according to the specific
interconnection topology, such basic building blocks.
The computation assigned to each processor is modelled, in general, as a set
of concurrent tasks performing cyclic activities. Those activities include a
local operation phase, whose duration is modelled by a stochastic variable,
exponentially distributed with parameter λ, followed by a request for service
addressed with equal probability to one of the neighbours. Service time is
modelled by a stochastic variable, exponentially distributed with parameter
µ. Thus, each processor must provide service to requests coming from any
of its immediate neighbours. In these models we do not explicitly represent
communication activities: the time required to perform sending and receiv-
ing operations is considered part of the service requesting and service giving
tasks.