flow analysis
- average time it takes between the moment the entire process starts and the moment it completes
-waiting time + processing time
= Theoretical cycle time (TCT)
(processing time; average time a case would take it there was no waiting time at all)
-CT efficiency = Ratio of overall processing time, referred to as theoretical cycle time (TCT), relative to the overall CT
critical path method
- critical path → sequence of process that determines the theoretical cycle time of the process
-identifies the critical path based on the notions of:
● early start/finish → forward pass
● late start/finish → backward pass
Little’s law
- total cycle time of a process is related to the arrival rate 𝜆 and the work-in-process WIP
arrival rate= avg nº of new process instances
WIP= avg nº of active process instances
characteristics of little’s law
Little’s law holds for any stable process (the amount of work doesn’t grow beyond control)
capacity and bottlenecks
Theoretical capacity= max nº of instances that can be completed per time unit by a resource pool (p)
-characteristcs:
● theoretical capacity of a resource pool implies that this pool is working at full capacity
● resource pool with the minimum theoretical capacity is called the bottleneck of a process
limitations of flow analysis
- Presented equations for calculating cycle time (CT) work only for block-structured process models
-Need to estimate the average CT of each task in the process model:
2 approaches:
1. to address this obstacle is based on interviews with, and/or observations of, process participants
- to collect logs from the IT systems used in the process
- Critical assumption that level of resource contention are stable over the long run
queueing theory
Collection of mathematical techniques to analyze systems with resource
contention, which inevitably leads to queues
● expected length (Lq)
● expected waiting time (Wq)
queuing system
consists of:
● 1 or multiple queues
● service that is provided by one or multiple servers
● elements inside a queue = jobs or customers
system types
-Single-line → M/M/1
-Multi-line → M/M/c (c = number of servers)
limitations of queuing analysis
- Assumption that inter-arrival times follow a negative exponential distribution
–> shorter inter-arrival times more likely
-Presented queuing analysis techniques can only deal with one process task at a time
–> queuing network more suitable
process simulation
use the process simulator for:
- generating a large number of hypothetical instances of a process
- executing these instances step-by-step
- recording each step in this execution
output of a simulator includes
-logs of the simulation
-statistics of cycle tymes, avg times, avg resource utilization
input parameters
-processing time of each task
-resource pool responsible for performing a given task
-branching probability for every gateway
-starting date and time of simulation
common probability distributions
- fixed values (rare)
- exponential distribution
- normal distribution
