The KendallLee Notation for Queuing Systems Mohamad Ayache

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The Kendall–Lee Notation for Queuing Systems Mohamad Ayache 16701680

The Kendall–Lee Notation for Queuing Systems Mohamad Ayache 16701680

• The notation is used to describe a queuing system in which all

• The notation is used to describe a queuing system in which all arrivals wait in a single line until one of s identical parallel servers is free. Then the first customer in line enters service, and so on. (Assume for FCFS)

To describe such a queuing system, Kendall (1951) devised the following notation. Each queuing

To describe such a queuing system, Kendall (1951) devised the following notation. Each queuing system is described by six characteristics: 1/2/3/4/5/6 Arrival/Service/Servers/Discipline/Customers/Popula tion

Arrival process M=Interarrival times are independent, identically distributed (iid) random variables having an exponential

Arrival process M=Interarrival times are independent, identically distributed (iid) random variables having an exponential distribution. D=Interarrival times are iid and deterministic. Ek=Interarrival times are iid Erlangs with shape parameter k. GI=Interarrival times are iid and governed by some general distribution. Arrival/Service/Servers/Discipline/Customers/Popula tion

Service time M =Service times are iid and exponentially distributed. D=Service times are iid

Service time M =Service times are iid and exponentially distributed. D=Service times are iid and deterministic. E =Service times are iid Erlangs with shape parameter k. G=Service times are iid and follow some general distribution. k Arrival/Service/Servers/Discipline/Customers/Popula tion

Number of parallel servers Arrival/Service/Servers/Discipline/Customers/Popula tion

Number of parallel servers Arrival/Service/Servers/Discipline/Customers/Popula tion

Queue discipline FCFS=First come, first served LCFS=Last come, first served SIRO=Service in random order

Queue discipline FCFS=First come, first served LCFS=Last come, first served SIRO=Service in random order GD=General queue discipline Arrival/Service/Servers/Discipline/Customers/Popula tion

Maximum allowable number of customers in the system Arrival/Service/Servers/Discipline/Customers/Popula tion

Maximum allowable number of customers in the system Arrival/Service/Servers/Discipline/Customers/Popula tion

Size of the population from which customers are drawn Arrival/Service/Servers/Discipline/Customers/Popula tion

Size of the population from which customers are drawn Arrival/Service/Servers/Discipline/Customers/Popula tion

Company A has 1000 employees and 50% of them are workers. A queue system

Company A has 1000 employees and 50% of them are workers. A queue system serves only workers. The arrival process is exponential. Service process have erlang distribution with shape parameter 3. First in first out. 5 servers are available. Arrival/Service/Servers/Discipline/Customers/Popula tion M/E 3/5/FCFS/500/1000

Health clinic M/E 2/8/FCFS/10/∞ 8 doctors, exponential interarrival times, twophase Erlang service times, an

Health clinic M/E 2/8/FCFS/10/∞ 8 doctors, exponential interarrival times, twophase Erlang service times, an FCFS queue discipline, and a total capacity of 10 patients.

M/M/1/GD/∞/∞ Can be written as M/M/1

M/M/1/GD/∞/∞ Can be written as M/M/1

Thank you Feel free to ask any questions related to the subject

Thank you Feel free to ask any questions related to the subject