| Possible applications of queuing theory |
Different
|
Queuing | System |
| M/M/1/GD/inf/inf | M/M/1/GD/C/inf | M/M/S/GG/inf/inf | |
| Given: | |||
| arrival rate | |||
| service rate | |||
| number of servers | |||
| limit on number in system, queue capacity | |||
| Can find the following information: | |||
| steady state condition | |||
| effective arrival rate, those really entered to the system | |||
| effective service rate, those being served and left system | |||
| average number in queue | |||
| average number in system | |||
| average number in sever | |||
| average waiting time in queue | |||
| average waiting time in system | |||
| average waiting time in server (service time) | |||
| balk rate, lost customer rate | |||
| server utilization | |||
| probability that: | |||
| the server is idle | |||
| a specific server is idle | |||
| the system is empty | |||
| a customer has to wait | |||
| a customer has to wait more than T time duration in system | |||
| a customer has to wait more than T time duration in queue | |||
| there are less than X customers in the system | |||
| probability of having X customers in the system | |||
| probability of having X customers in the queue | |||
| Can consider the following applications: | |||
| total average cost of ………..…… per unit of time: | |||
| customers waiting time in system (queue) | |||
| servers | |||
| customer
dissatisfaction when has to wait
(no matter how long) |
|||
| loss of customer (when balking) | |||
| space allocation for waiting line | |||
| service level (for example): | |||
| queue capacity to accommodate customers 90% of times | |||
| probability of having more than Y customers in system is 0.1 | |||
| space required for line up in layout design | |||
| space required for servers in layout design | |||
| forecasting of required budget for equipment and space | |||
| sever level: | |||
| under-utilized servers, therefore reduce the number | |||
| over-utilized servers, therefore increase the number | |||
| sensitivity analysis: | |||
| find the best number of servers | |||
| find the best queue capacity for system | |||
| find the effect of changes in arrival rate | |||
| find the effect of changes in service rate | |||
Last Updated: May 1999