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

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

3. 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?

4. 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

5. 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

6. 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

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

8. 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

9. One Open Cash Register ave_service_ti me = 0.8736 ave_wait_time = 19.4549 ave_total_tim e =19.9618

10. Two Cash Registers Open ave_service_ti me =0.7215 ave_wait_time =11.9748 ave_total_tim e =12.3420

11. Cash Register at Each Station ave_service_time = 0.8599 ave_wait_time = 21.2689 ave_total_time =21.8126

12. 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