A bank has two categories of customers, regular and first-tier customers. In its bank branch it has three servers (R1, R2 and R3) that serve regular customers and two servers that serve premier customers (P1 and P2). There are two

A bank has two categories of customers, regular and first-tier customers. In its bank branch it has three servers (R1, R2 and R3) that serve regular customers and two servers that serve premier customers (P1 and P2). There are two separate queues for main and regular customers. When a main client arrives, if P1 or P2 is free, it will start service immediately on P1 or P2. If P1 and P2 are busy, but R1, R2, or R3 are free, then the primary client immediately transitions to service on R1, R2, or R3. If R1, R2, and R3 are busy, the arriving primary client will join the primary queue. When a regular customer arrives, they can be served by R1, R2, or R3, if one is available. If all R1, R2, and R3 are busy, and if any of the primary servers (P1 or P2) are free, it will be served by any of the main free servers. If all five servers are busy, the regular that arrives will join the regular queue. As long as the main customer queue is empty and P1/P2 is free, if there is a queue for regular customers, P1/P2 will serve regular customers until the next main customer arrives. Similarly, as long as R1, R2, or R3 is free and there is no regular waiting, it can serve the top customers (if there are any in the queue), until the next regular arrives. The service times of P1 and P2 are distributed identically, and since the bank assigns the most experienced teller to serve the main customers, they serve twice as fast as R1, R2 or R3. The service times of R1, R2 and R3 are distributed identically. Clients enter the bank according to the Poisson processes at a rate of 4 per hour for premier clients and 8 per hour for regular clients. 

Questions

1. Define the states and events for this system. 

2. Draw the flowcharts for running the events (one for each type of event).

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