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Question of the Day
TBD
Assigned Reading
Chapter 3.1 - 3.2. ECE 6400 students should also read Chapter 4.4 as an independent study.
Queuing Models
The goal of this module is to introduce the simplest way in which we can model the behavior of a link.
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- First-come, first-served (FCFS)
- process customers in order of arrival
- most common queueing discipline
- e.g. linked list data structure where 0th element is always removed
- Last-come, first-served (LCFS)
- process most recent customer to have arrived
- could lead to starvation
- e.g. use of a stack via push and pop (brings back memories from x86 assembly, right?
)
- Round robin (RR)
- Poll from separate queues in a circular manner
- Processor sharing (PS)
- Time shared access to server
- All customers served simultaneously (but a little at a time)
- e.g. a CPU on a general purpose machine where the OS schedules tasks
- Random
- Priority
- Multiple classes of customers
- Some classes have higher or lower priority than others
- Higher priority customers receive "better" service
- Lower priority customers receive "worse" service
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Thus, the average number of customers in the system during the interval [0, t] is:
Consider all customers in system at time t (i.e. N(t) customers). Let RN(t) denote the total time after t that those N(t) customers spend in the system. The average time spent in the system by all customers arriving in the interval [0, t] is:
So:
and:
For the stable system we are concerned with, the following limits hold:
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