COMPACT MODELS OF RANDOM POLLING SYSTEMS - Modelling with Generalised Stochastic Petri Nets - page 204

Table 9.1: Characteristics of the timed transitions in the GSPN model of a
cyclic single-server polling system (q = 0, 1, 2, 3)

transition rate semantics

T (q) λ (q) single-server

a

T (q) µ (q) single-server s

T (q) ω (q) single-server w

Table 9.2: Characteristics of the immediate transitions in the GSPN model
of a cyclic single-server polling system (q = 0, 1, 2, 3)

transition weight priority ECS

t (q)

1 2 q + 1 s

t (q)

1 1 q + 5 w

The characteristics of the timed and immediate transitions in the GSPN
model in Fig. 9.2 are summarized in Tables 9.1 and 9.2, respectively.
The GSPN model in Fig. 9.2 provides a more detailed description of the sys-
tem behaviour with respect to the queuing representation in Fig. 9.1: from
the GSPN model we see that queues have finite capacity, that the server can
serve at most one customer before leaving a queue (this is a specification of
the 1-limited service discipline); furthermore, the GSPN description makes
it clear that the server does not stop at a queue if no service can be provided,
and that the server movement consumes time.
To completely specify the behaviour of a single-server polling system, it is
necessary to define several parameters and operating rules:

• the number of queues

• the storage capacity at each queue, which can be either finite or infinite

• the customer arrival process at each queue

• the queuing discipline at each queue, which is normally assumed to be
FCFS

• the customer service times at each queue, which can be random vari-
ables with general distributions

• the service discipline at each queue, which specifies the customers that
can be served when a server visits a queue; the distinction among