APPLICATION OF QUEUING THEORY TO WASHU DINING

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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?.

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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
• 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
One Open Cash Register

ave_service_time = 0.8736

ave_wait_time = 19.4549

ave_total_time =19.9618

Two Cash Registers Open

ave_service_time =0.7215

ave_wait_time =11.9748

ave_total_time =12.3420

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