Productionline (PL-Model)

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1 General Description of the productionline

A production line of a manufacturing plant consists of N service queues arranged in a row, that is, parts leaving a queue after service are immediately transferred to the next queue (see Figure 1). All queues have a finite capacity K. Arrivals of parts to the first queue occur according to a Poisson process with rate lambda. For subsequent queues we assume arriving parts to get lost if the queue buffer is occupied. Each queue comprises a single server with first-come, first-served (FCFS) service discipline and exponentially distributed service time. The throughput of the productionline can be easily measured as the throughput of machine n.

Figure 1: Class based queuing model

2 Description of the model

Though the productionline is defined as a model with a variable number N of service queues, a separate petrinet model for each number of machines has to created. Figures 2 and 3 represent productionlines with N = 2 and N = 3. Each service queue has its own number and the names of all components of a service queue end with this number. Therefore a general description of the model which was given in the previous chapter and the description of one service queue provides all information needed.

New tokens arrive at the place Parts? either from the external storage External or the previous queue. Note that the ? stands for the number of the queue. If the place FreeBuffers? is not empty the new token is moved into the queue Queue? otherwise it is rejected and moved back to the external storage Eternal. If the machine is currently idle which means place ToServe? is empty a token is moved from the queue Queue? to the place ToServe?. When the token in place ToServe? is served by transition service? it is moved either to the next queue or the production is finished and it is moved back to the external storage External.

Figure 2: APNN-Model of a two server Productionline

Figure 3: APNN-Model of a three server Productionline

3 Tables of places and transitions

If a '?' appears at the end of a name it is a replacement for the number of the machine. As all places and transitions have equal values at the beginning.

3.1 Places

3.2 Immediate transitions

3.3 Timed transitions