         WAITING LINE ANALYSIS

WAITING LINES OCCUR IN ALMOST ANY SYSTEM FROM THE SUPERMARKET
CHECKOUT COUNTER TO THE RUNWAY AT AN AIRPORT. IN ANALYZING
A WAITING LINE SITUATION, ON THE ONE HAND LONG WAITING LINES
CAUSE LOSS OF BUSINESS EVEN IF ONLY DUE TO CUSTOMER DISSAT-
FACTION WHILE INCREASING SERVICE INCREASES COSTS. IN THIS
WE ASSUME THERE IS A SINGLE SERVER(E.G. CHECKOUT PERSON),
WHO CAN SERVE,ON AVERAGE, A GIVEN NUMBER OF CUSTOMERS PER
TIME. THE CUSTOMERS ARRIVE RANDOMLY AT SOME OTHER AVERAGE RATE.
THE WAITING LINE IS FIRST COME-FIRST SERVED. WE EXAMINE THE
PROBABILISTIC CHARACTERISTICS OF THE WAITING LINE OR QUEUE
AS IT IS GENERALLY CALLED. THE AVERAGE SERVICE RATE IS THE
MEAN SERVICE RATE WHILE THE AVERAGE ARRIVAL RATE IS THE MEAN
ARRIVAL RATE.
PRESS ENTER TO CONTINUE? 
ONE REQUIREMENT IS THAT THE MEAN SERVICE RATE BE GREATER
THAN THE MEAN ARRIVAL RATE. OTHERWISE THE QUEUE WOULD GET
INFINITELY LONG.

WHAT AVARAGE MEANS IS SOMETIMES LONGER,SOMETIMES SHORTER BUT
IF SOMEONE LOKKED AT THE WAITING LINE EVERY DAY FOR A MONTH
THEN THE AVERAGE(MEAN) QUEUE LENGTH FOR THE MONTH WOULD BE
CLOSE TO WHAT WAS COMPUTED HERE.
PRESS ENTER TO BEGIN? 
THE FOLLOWING ARE IN NUMBER PER UNIT TIME

     ENTER MEAN ARRIVAL RATE OF UNITS? 34
     ENTER MEAN SERVICE RATE OF UNITS? 45

AVERAGE LENGTH OF THE QUEUE      =  2.33535 
AVERAGE LENGTH OF THE SYSTEM     =  3.09091 
AVERAGE WAITING TIME ON QUEUE    =  6.86869E-2 
AVERAGE TIME WAITING IN SYSTEM   =  9.09091E-2 
PROBABILITY SYSTEM IS BUSY       =  .755556 

SYSTEM TIME IS WAITING TIME PLUS SERVICE TIME.

PRESS ENTER FOR MORE? -1
