ECE 658: Performance Evaluation and Simulation
Electrical and Computer Engineering,
University of Cyprus
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Homework Problem Set 1
 
1.
For each of the following queueing systems, define a state automaton and construct a state transition diagram showing all feasible events
  • A computer processor is preceded by a queue which can accommodate one job only (so that the total capacity of the system two jobs). Two different types of jobs request service from the processor with type one having higher priority than type 2. Thus, if a type 1 job arrives and finds a type 2 job in service, it preempts it: The type 2 job is returned to the queue, and the type 1 job receives service. If any job arrives and finds the system full, it is rejected and lost.
  • A system consists of three servers. New arriving customers first enter the queue preceding server 1, and after completing service they are routed to either server 2 or 3. The routing policy is to always send a customer to the server with the shortest queue, and in case of a tie to send to server 2. Customers completing service at servers 2 and 3 leave the system. A customer arriving from the outside is accepted into the system only as long as the total number of customers present is less than 3; otherwise customers are rejected.
2. A computer processor is preceded by a queue which can accommodate one job only (so that the total capacity of the system two jobs). Two different types of jobs request service from the processor with type one having higher priority than type 2. Thus, if a type 1 job arrives and finds a type 2 job in service, it preempts it: The type 2 job is returned to the queue, and the type 1 job receives service. If any job arrives and finds the system full, it is rejected and lost. Model this systems using a timed Petri net.
   
  last updated September 27, 2006