ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 113

p act1 p act2

T req1 λ 1 λ 2 T req2

p idle

p req1 p req2

T str1 α 1 α 2 T str2

p acc1 p acc2

T end1 µ 1 µ 2 T end2

Figure 6.1: The SPN description of shared memory system

common shared memory. The net comprises seven places and six timed tran-
sitions with single-server semantics; for convenience the SPN is depicted in
Fig. 6.1 and the additional specifications are contained in Tables 6.1 and

6.2.
Starting from the initial marking shown in Fig. 6.1, in which the two pro-
cessors are both in a locally active state (p act1 + p act2 + p idle ), a possible
evolution of the SPN marking that focuses on the processing cycle of pro-
cessor 1, may be the following. Processor 1 works locally for an exponentially
distributed random amount of time with average 1/λ 1 , and then requests
an access to the common memory. Transition T req1 fires, and the token con-
tained in p act1 is removed while a token is added in p req1 . Since the common
memory is available (place p idle is marked), the acquisition of the memory
starts immediately and takes an average of 1/α 1 units of time to complete;
this is represented by the firing of transition T str1 whose associated delay
has a negative-exponential distribution with rate α 1 ; when transition T str1
fires, one token is removed from place p req1 and another token is deposited
into place p acc1 , where it stays for the entire time required by the first pro-
cessor to access the common memory. Such a time lasts on the average 1/µ 1
units of time, and ends when transition T end1 fires returning the net to its
initial state. Obviously, a similar processing cycle is possible for processor
2 and many interleavings between the activities of the two processors may