Week 3 - MoPs Flashcards
What are the six basic measures of system performance (MoPs)?
• Arrival time - the time at which a customer arrives for service
• Departure time - the time at which a customer departs from the system
• Departure time from queue - the time at which a customer departs from the queue
• Time in queue - time spent in the queue
• Service time - time being served
• Time in system - time from arrival to depart
Other measures of system performance (5)
• Arrival rate - the rate at which customers arrive for service
• Departure rate - is the rate at which customers depart from the system
• Service rate - the rate at which customers are served
• Utilisation - the time the server spent doing useful work
• Queue length - number of customers in the queue
Relationship between time and costs with measure of system performance (3)
• Time in queue can identified by converting waiting time to waiting costs
• Time in servers can be identified by converting service time to service costs
• Time in system can be identified by converting (waiting time + service time) to (waiting costs + service costs) as well as efficiency
formulas for utilisation (3)
• Server working - (waiting for work - being idle - being blocked)
• Time working - (time waiting for work - time being idle - time being blocked)
• Cost working - (cost waiting for work - cost being idle - cost being blocked)
• Being blocked e.g massive queue where there you can’t take breaks and start to feel tired leading to delays in a service
Formula for cost of working
•
How can MoPs be classified? (2)
• Customer MoPs - concerned with what customers care about such as time in queue and service time
• Server MoPs - Concerned with what servers care about such as cost of service, attracting and retaining customers
What are cumulative arrivals?
Is the accumulation of arrivals over a certain period of time
What are cumulative departures?
Is the accumulation of departures over a certain period of time
What is A(t)?
Stands for cumulative arrivals from time 0 to time t
What is Ds(t)
Standards for cumulative departures from server from the time 0 to time t
What is Dq(t)?
Stands for cumulative departures from queue from time 0 to time t
Formula for customers in the queue (queue length)
• Lq(t) = A(t) - Dq(t)
• Lq(t) is the queue length, A(t) is the cumulative arrival from time 0 to time t , Dq(t) is the cumulative departure time from time 0 to time t
Formula for the number of customers in the system Ls(t)
• Ls(t) = A(t) - Ds(t)
• A(t) is the accumulative arrivals from time 0 to time t, Ds(t) is the accumulative departures from the system from time 0 to time t
3 basic properties of typical queueing systems
• A customer cannot leave the queue before it/he/she arrives
• A customer cannot leave the system before it/he/she leaves queue
• Lq(t) (queue length) and Ls(t) (number of customers in a system) are always greater than or equal to zero
What is Wq(n)?
Is the time in queue for nth customer to arrive in the queue
What is the formula for the average time in queue (wq)
What is Ws(n)?
Is the time in system, for nth customer to arrive at the system
What is the formula for the average time in system (Ws)
Formula for the standard deviation of average time in queue (σwq)
Formula for the standard deviation of average time in system (σWs)
w
What is Ŵq
Is the number of customers x time in queue
What is Ŵs?
Is the number of customers x time in system
Formula for the average queue length using Ŵq and Ŵs
Lq = Ŵq/time interval or Lq = Ŵs/time interval
• E.g 15 customers x 2minutes / 30 minutes time interval = 1 customer
Formula for the arrival rate λ
• Is the number of customers/time period
• λ = N/(b-a)
Formulas for queue length and average time in queue using the arrival rate (2) (Little’s formula)
• Lq = Wq x λ
• Wq = Lq/λ
example of illustrating queueing system behaviour (5)
• 1st customer comes and is served for 5 minutes then leaves
• 2nd customer in the queue for 15 minutes and is then served for 5 minutes then leaves
• 3rd customer queued for 5 minutes and was in the server for 15 minutes
• 4th customer queued for 25 minutes and then was served for 10 minutes
• 5th customer queued for 25 minutes and we’re then served for 5 minutes
