Case Study for Restaurant Queuing Model
2011 International Conference on Management and Artificial Intelligence IPEDR vol.6 (2011) © (2011) IACSIT Press, Bali, Indonesia
Case Study for Restaurant Queuing Model
Mathias Dharmawirya
School of Information Systems Binus International – Binus University Jakarta, Indonesia mdharmawirya@binus.edu
Erwin Adi
School of Computer Science Binus International – Binus University Jakarta, Indonesia eadi@binus.edu busy fast food restaurant [3], as well as to increase throughput and efficiency [5]. This paper uses queuing theory to study the waiting lines in Sushi Tei Restaurant at Senayan City, Jakarta. The restaurant provides 20 tables of 6 people. There are 8 to 9 waiters or waitresses working at any one time. On a daily basis, it serves over 400 customers during weekdays, and over 1000 customers during weekends. This paper seeks to illustrate the usefulness of applying queuing theory in a realcase situation. II. QUEUING THEORY In 1908, Copenhagen Telephone Company requested Agner K. Erlang to work on the holding times in a telephone switch. He identified that the number of telephone conversations and telephone holding time fit into Poisson distribution and exponentially distributed. This was the beginning of the study of queuing theory. In this section, we will discuss two common concepts in queuing theory. A. Little’s Theorem Little’s theorem [7] describes the relationship between throughput rate (i.e. arrival and service rate), cycle time and work in process (i.e. number of customers/jobs in the system). This relationship has been shown to be valid for a wide class of queuing models. The theorem states that the expected number of customers (N) for a system in steady state can be determined using the following equation: (1) Here, λ is the average customer arrival rate and T is the average service time for a customer. Consider the example of a restaurant where the customer’s arrival rate (λ) doubles but the customers still spend the same amount of time in the
Case Study for Restaurant Queuing Model
Mathias Dharmawirya
School of Information Systems Binus International – Binus University Jakarta, Indonesia mdharmawirya@binus.edu
Erwin Adi
School of Computer Science Binus International – Binus University Jakarta, Indonesia eadi@binus.edu busy fast food restaurant [3], as well as to increase throughput and efficiency [5]. This paper uses queuing theory to study the waiting lines in Sushi Tei Restaurant at Senayan City, Jakarta. The restaurant provides 20 tables of 6 people. There are 8 to 9 waiters or waitresses working at any one time. On a daily basis, it serves over 400 customers during weekdays, and over 1000 customers during weekends. This paper seeks to illustrate the usefulness of applying queuing theory in a realcase situation. II. QUEUING THEORY In 1908, Copenhagen Telephone Company requested Agner K. Erlang to work on the holding times in a telephone switch. He identified that the number of telephone conversations and telephone holding time fit into Poisson distribution and exponentially distributed. This was the beginning of the study of queuing theory. In this section, we will discuss two common concepts in queuing theory. A. Little’s Theorem Little’s theorem [7] describes the relationship between throughput rate (i.e. arrival and service rate), cycle time and work in process (i.e. number of customers/jobs in the system). This relationship has been shown to be valid for a wide class of queuing models. The theorem states that the expected number of customers (N) for a system in steady state can be determined using the following equation: (1) Here, λ is the average customer arrival rate and T is the average service time for a customer. Consider the example of a restaurant where the customer’s arrival rate (λ) doubles but the customers still spend the same amount of time in the