Timed net with choice probability and its minimum cycle time—The case of location-based service

For performance analysis of computer systems, the minimum cycle time method has been widely used. The minimum cycle time method is a mathematical technique with which we can find the minimum duration time needed to fire all the transitions at least once and coming back to the initial marking in a timed net. A timed net is a modified version of a Petri net, where a transition is associated with a delay time. In the real world, an event A is usually in the conflict relation with another event B, i.e. if event A is selected to occur then event B cannot occur. When events A and B are in conflict, they are usually associated with probability of choices. However, a timed net is not equipped with any facility of specifying probabilities of event choices. Therefore, the minimum cycle time method applied on a timed net is apt to overlook probabilities of event choices and yield a wrong result. We are proposing ‘Timed net with Choice Probability’, where a transition can be associated with both delay time and a probability of choice. We also introduce an algorithm for minimum cycle time analysis for ‘Timed net with Choice Probability’. As an example of application, we are performing an analysis of a location-based service system using ‘Timed net with Choice Probability’.