The objective of this model is to choose the number of servers in a queuing system that minimizes total cost. If all servers are busy when a customer arrives, then the customer is lost. Total cost is composed of the cost of hiring our servers plus the expected cost of lost customers. The @PEL function is used to get the fraction of customers lost due to all servers being busy when they arrive.

MODEL:

! Model of a queuing system with N servers, each of

 which costs $17/hour. Arrivals occur at a rate of

 70 per hour in a Poisson stream. Arrivals finding

 all servers busy are lost. A lost customer costs

 $35. The average time to process a customer is 5

 minutes;

 

! Minimize total cost =

 service costs + lost customer cost;

   [COST]  MIN = SCOST + LCOST ;

 

! Cost of servers;

   SCOST = 17 * N ;

 

! Cost of lost customers;

   LCOST = 35 * 70 * FLOST ;

 

! The fraction of customers lost;

   FLOST = @PEL( 70 * 5 / 60 , N);

END

Model: QUEUEL