Overview%20of%20Queueing%20Systems

1
Overview of Queueing Systems

• Michalis Faloutsos
• Archana
• Yordanos
• The web

2
Overview of queueing concepts
Exponential Distribution
Memoryless
The probability of having an arrival(departure)
at time x.
Poisson Process. with mean arrival rate l
The probability of having k events.
Interarrival time in a Poisson process is
exponential
tnis the interarrival tn1-tn
3
Littles Theorem
N
l
T
customer arrival rate N average number of
customers in system T average delay per customer
in system Littles Theorem System in
steady-state
l
4
Queueing Systems

• n number of customers in the system (including
  queue server)
• pn steady state probability of finding n
  customers in the system
• ?? ?/? Traffic rate (traffic intensity)
• M stands for Markovian'',

5
Modeling a queueing system

• What goes left, must come right
• of transitions ? of transitions ?

Pi are probabilities
6
Basic formulas
Expected number of customers in the system
Expected time a customer spends in the system
Expected time a customer spends in the queue
Expected number of customers in the system