Graphics Programs Reference
In-Depth Information
Figure 9.1:
Queuing representation of a cyclic single-server polling system
A single-server cyclic polling system (the simplest and most common polling
system) comprises a set of waiting lines that receive arrivals from the exter-
nal world, and one server that cyclically visits the queues, providing service
to customers that afterwards depart from the system. The usual pictorial
representation of this behaviour in queuing notation is shown in Fig.
9.1
in the case of four queues.
The GSPN description of the same system is
provided in Fig.
9.2.
It can be observed that the GSPN model in Fig.
9.2
comprises four replicas
of the subnet that describes the internal organization of each individual
queue (enclosed within ovals), interconnected by four replicas of the subnet
that describes the movement of the server from a queue to the next one.
Customers waiting for a server are queued in place p
(q)
q
, while a token in place
p
(q
p
represents the server when polling queue q. The two immediate transi-
tions t
(q)
s
) = 2, Π(t
(q
w
) =
1). Transition t
(q
s
fires if the server finds a waiting customer when it polls
the queue, so that service can be provided; if t
(q
s
cannot fire when the queue
is polled by a server, i.e., if the server finds no waiting customers, then t
(q)
and t
(q)
have priorities 2 and 1, respectively (Π(t
(q)
s
w
w
fires, and the server moves to the next queue.
One token in place p
(q
s
represents a customer of queue q being served, as
well as the server when providing service at queue q. T
(q)
is timed with a
s
delay equal to the customer service time.
The server moves to place p
(q
w
at the end of the visit at queue q (after the
service completion represented by the firing of T
(q)
, if a waiting customer
s
was found; after the firing of t
(q)
if no waiting customer was found). From
w
p
(q)
w
the server walks to the next queue. Transition T
(q
w
models the server
walk time from queue q to the next queue in the cyclic schedule.
1
The superscript (
q
) indicates that the place (or transition) belongs to the model of
queue
q
.
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