3.6. Consider solving the set of steady-state equations for a system with a limit on the...

 

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3.6. Consider solving the set of steady-state equations for a system with a limit on the number of jobs allowed (example M/M/1/3). Suppose there are nmax steady- state equations derived from the flow-in equals flow-out approach. Show that if only these equations (omitting the norming equation) are used and if they are linearly independent, then the solution for pn cannot satisfy the conditions for a pmf. This result leads to the conclusion that this set of equations must be dependent and, there- fore, the norming equation must be used in place of one of the other equations. 3.6. Consider solving the set of steady-state equations for a system with a limit on the number of jobs allowed (example M/M/1/3). Suppose there are nmax steady- state equations derived from the flow-in equals flow-out approach. Show that if only these equations (omitting the norming equation) are used and if they are linearly independent, then the solution for pn cannot satisfy the conditions for a pmf. This result leads to the conclusion that this set of equations must be dependent and, there- fore, the norming equation must be used in place of one of the other equations.

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In queueing theory the MM13 system represents a singleserver queue with a maximum of 3 jobs allowed in the system This system follows the Markovian pr... View the full answer