APPLICATION OF QUEUING THEORY TO WASHU DINING Presented

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

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

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

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

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 Mc. Donalds vs. Taco Bell Has

Queuing Theory Continued Many applications to everyday life Mc. Donalds 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

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 1/2λ

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

OUR PROCESS Determine the probability of a customer choosing a station Determine the food

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 _time = 0. 8736 ave_wait_ti me = 19. 4549

One Open Cash Register ave_service _time = 0. 8736 ave_wait_ti me = 19. 4549 ave_total_ti me =19. 9618

Two Cash Registers Open ave_service _time =0. 7215 ave_wait_ti me =11. 9748 ave_total_ti me

Two Cash Registers Open ave_service _time =0. 7215 ave_wait_ti me =11. 9748 ave_total_ti me =12. 3420

Cash Register at Each Station ave_service_ti me = 0. 8599 ave_wait_time = 21. 2689

Cash Register at Each Station ave_service_ti me = 0. 8599 ave_wait_time = 21. 2689 ave_total_time =21. 8126

Conclusion Two cash registers are faster than one Cash registers at each station cause

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