We study a Petri net model of a system composed of two processes sharing a resource. Conflicts may occur over the usage of the shared resource, thus making the system nondeterministic. Therefore, in the context of minimax algebra, it cannot be formulated as a linear system in order to compute its performance measures. However, if the sequence by which the resource is allocated to the two processes is known, we can transform the system into a decision-free net. For this system with an imposed constraint on the resource allocation frequencies, we show that the optimal allocation sequence is the most regular integer sequence satisfying that constraint. We also discuss the periodic behavior of this system under no constraints on the resource allocation frequencies. >
[1]
Kathryn E. Stecke,et al.
Dynamic analysis of repetitive decision-free discrete-event processes: applications to production systems
,
1991
.
[2]
Jean-Marie Proth,et al.
Performance evaluation of job-shop systems using timed event-graphs
,
1989
.
[3]
C. V. Ramamoorthy,et al.
Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets
,
1980,
IEEE Transactions on Software Engineering.
[4]
Tadao Murata,et al.
Petri nets: Properties, analysis and applications
,
1989,
Proc. IEEE.
[5]
Bruce E. Hajek,et al.
Extremal Splittings of Point Processes
,
1985,
Math. Oper. Res..