Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Danish
mathematician, statistician and
engineer, who invented the fields of traffic engineering and queueing theory
David George Kendall FRS[2] (15 January 1918 – 23 October 2007)[3] was an English statistician and
mathematician, known for his work on probability, statistical shape
analysis, ley lines and queueing theory
Queuing Theory is one of the most commonly used mathematical tool for the performance evaluation of any complex systems where the reliability and efficiency of the
components play a very important role
For the better understanding of the dynamic behavior of the involved processes one have to deal with constructions of mathematical models which describe the
stochastic service of randomly arriving requests
Elements of queuing system:
The Customer The server
First in first out
This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first.
Last in first out
This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first. Also known as a stack.
Processor sharing
Service capacity is shared equally between customers
Priority
Customers with high priority are served first. Priority queues can be of two types, non-preemptive (where a job in service cannot be interrupted) and preemptive (where a job in service can be interrupted by a higher priority job). No work is lost in either model.
Shortest job first
The next job to be served is the one with the smallest size
Preemptive shortest job first
The next job to be served is the one with the original smallest size
Shortest remaining processing time
The next job to serve is the one with the smallest remaining processing requirement.
Focal Concern: MEASURES OF PERFORMANCE
Customer Measure of Performance
• Time in Queue
• Waiting cost
• Proportion of work completed on time
• Tardiness
Server Measure of Performance
• Service time
• Proportional utilization
• Throughput
• Arrival Rate
Chapter 1 all Chapter 2 all
Chapter 3 arrival process (all) 3.1
3.2 3.3 3.4 3.5
- uts
---Chapter 5 Performance Measurements
s/d 5.4
Chapter 6 Non stationary Poisson process
6.1
Chapter 9 9.1
