APPLICATION OF QUEUING THEORY TO WASHU DINING Presented by: Rohit Ray and Antonia Ferguson

INTRODUCTION  Village Dining Area  5 food areas  Grill  Stir fry  Specialty  Salad/Deli  Grocery  One or two cash registers open

IS THE CHECKOUT METHOD THE MOST EFFICIENT?  Should both cash registers be open?  Would it be more efficient for there be cash registers at each food station?

QUEUING THEORY  Agner Krarup Erlang  Published first paper on queuing theory in 1909  Mathematical study of wait lines  Allows for mathematical analysis of several related processes  Arrival  Weighting in line  Being served  Calculates  Average weight time in line  Number of people in line  Probability waiting a certain time to be served

Queuing Theory Continued  Many applications to everyday life  McDonalds vs. Taco Bell  Has been used to reduce time in:  Hospital wait rooms  Airports  Supermarkets  Printing queue

POISSON DISTRIBUTION Poisson Distribution Equation:  Queuing Theory is a Poisson distribution  Continuous limit of the discrete binomial distribution  Four requirements  ability to divide the time interval into subintervals  Probability of occurrence remains constant throughout interval  Probability of the same occurrence in a subinterval is small enough to be discarded  Occurrences are independent

POISSON CONTINUED  For one cashier the probability is 1/ λ  Two cashiers 1/2 λ

OUR PROCESS  Determine the probability of a customer choosing a station  Determine the food preparation time  Determine the average number of people entering the Village Dining area  MATLAB

One Open Cash Register ave_service_ti me = ave_wait_time = ave_total_tim e =

Two Cash Registers Open ave_service_ti me = ave_wait_time = ave_total_tim e =

Cash Register at Each Station ave_service_time = ave_wait_time = ave_total_time =

Conclusion  Two cash registers are faster than one  Cash registers at each station cause longer waiting times  The wait could be shorter with a queue line