Queueing systems Flashcards
How do continuous time Markov chains differ to discrete time Markov chains
in the fact that jumps from one state to another no longer happen at specified intervals but rather at unknown time. The event time is a random variable.
What type of distribution do we assign to the random time
Exponential
Equation for the time spent in a state in a Quang system with 2 options with params n and m
e^-(n+m)t
When is a poison process in steady state
When the rates at which the system enters and leaves state n are equal
Rate of entering a state is calculated by looking at the different states it can enter it from and multiplying the rate at which the process enters the state from there by the proportion of time the process is in that given state (and then summing the different routes).
For an arrival rate lambda, what is the expected time between arrivals
1/ lambda
What is the service rate, mu, and what does 1/ mu represent
The expected numb r of customers that can be served by one of the servers per unit time.
The expected service time per customer.
Equation for utilisation factor and what is it
Rho = lambda / s x mu
S= no servers Mu = service rate Lambda = arrival rate
Represents the fraction of the time we expect the service facility to be busy (i.e., at least one of the servers to be busy).
If a continuous random variable has the lack of memory property, what distribution does it have
Exponential
What’s little’s formula
Number of customers in a queue L is equal to arrival rate lambda times the average time in the system
L = λW
How to find expected queue length of a s-server system
Sum all of the state’s number of consumers i multiplied by the probability shifted up the queue by s (number of servers): p(i + s)
For Kendall’s notation what do M, D and G stand for
Memoryless (exponential)
Deterministic (not probabilistic)
General (unspecified)
How do continuous time Markov chains differ to discrete time Markov chains
in the fact that jumps from one state to another no longer happen at specified intervals but rather at unknown time. The event time is a random variable.
What type of distribution do we assign to the random time
Exponential
Equation for the time spent in a state in a Quang system with 2 options with params n and m
e^-(n+m)t
When is a poison process in steady state
When the rates at which the system enters and leaves state n are equal
Rate of entering a state is calculated by looking at the different states it can enter it from and multiplying the rate at which the process enters the state from there by the proportion of time the process is in that given state (and then summing the different routes).
