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# APPLICATION OF QUEUING THEORY TO WASHU DINING - PowerPoint PPT Presentation

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

• Village Dining Area

• 5 food areas

• Grill

• Stir fry

• Specialty

• Grocery

• One or two cash registers open

• Should both cash registers be open?

• Would it be more efficient for there be cash registers at each food station?

• 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

• 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 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

• For one cashier the probability is 1/λ

• Two cashiers 1/2λ

• 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

ave_service_time = 0.8736

ave_wait_time = 19.4549

ave_total_time =19.9618

ave_service_time =0.7215

ave_wait_time =11.9748

ave_total_time =12.3420

ave_service_time = 0.8599

ave_wait_time = 21.2689

ave_total_time =21.8126

• 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