The Kendall–Lee Notation for Queuing Systems
Description: The KendallLee Notation for Queuing Systems Mohamad Ayache 16701680 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
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slide1. The Kendall–Lee Notation for Queuing Systems Mohamad Ayache 16701680<br>
slide2. 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)<br>
slide3. 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/Population<br>
slide4. 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/Population<br>
slide5. Service time M =Service times are iid and exponentially distributed.
D=Service times are iid and deterministic.
Ek =Service times are iid Erlangs with shape parameter k.
G=Service times are iid and follow some general distribution. Arrival/Service/Servers/Discipline/Customers/Population<br>
slide6. Arrival/Service/Servers/Discipline/Customers/Population Number of parallel servers<br>
slide7. 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/Population<br>
slide8. Maximum allowable number of customers in the system Arrival/Service/Servers/Discipline/Customers/Population<br>
slide9. Size of the population from which customers are drawn Arrival/Service/Servers/Discipline/Customers/Population<br>
slide10. 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. M/E3/5/FCFS/500/1000 Arrival/Service/Servers/Discipline/Customers/Population<br>
slide11. Health clinic M/E2/8/FCFS/10/∞ 8 doctors, exponential interarrival times, two-phase Erlang service times, an FCFS queue discipline, and a total capacity of 10 patients.<br>
slide12. M/M/1/GD/∞/∞ Can be written as M/M/1<br>
slide13. Thank you Feel free to ask any questions related to the subject<br>
slide2. 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)<br>
slide3. 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/Population<br>
slide4. 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/Population<br>
slide5. Service time M =Service times are iid and exponentially distributed.
D=Service times are iid and deterministic.
Ek =Service times are iid Erlangs with shape parameter k.
G=Service times are iid and follow some general distribution. Arrival/Service/Servers/Discipline/Customers/Population<br>
slide6. Arrival/Service/Servers/Discipline/Customers/Population Number of parallel servers<br>
slide7. 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/Population<br>
slide8. Maximum allowable number of customers in the system Arrival/Service/Servers/Discipline/Customers/Population<br>
slide9. Size of the population from which customers are drawn Arrival/Service/Servers/Discipline/Customers/Population<br>
slide10. 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. M/E3/5/FCFS/500/1000 Arrival/Service/Servers/Discipline/Customers/Population<br>
slide11. Health clinic M/E2/8/FCFS/10/∞ 8 doctors, exponential interarrival times, two-phase Erlang service times, an FCFS queue discipline, and a total capacity of 10 patients.<br>
slide12. M/M/1/GD/∞/∞ Can be written as M/M/1<br>
slide13. Thank you Feel free to ask any questions related to the subject<br>