MAX PLUS ALGEBRA OF TIMED PETRI NET FOR MODELLING SINGLE SERVER QUEUING SYSTEMS

Abstract

This research modified a single server queuing system using timed Petri net. We add two places, a transition and its appropriate arcs. This research also considered all the holding times in the timed Petri net. We found that the Petri net is not stable but stabilizable according to Lyapunov stability criteria. The standard autonomous equation of the system is also determined. Furthermore, this system also has the eigen value which related to its periodical behavior, it is . This means that the periodical behavior of the system only depends on the value of holding times of place W, R, B, and I.

Keywords

• timed petri net
• single server
• queuing system
• lyapunov stability
• standard autonomous equation
• eigen value