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### 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 1/2λ

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

Cash Register at Each Station

ave_service_time = 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 longer waiting times
- The wait could be shorter with a queue line

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