little's law and predictability - daniel vacanti - agile israel 2014
TRANSCRIPT
A predictable process is one that
behaves the way it is expected to
Predictability is the degree to
which we can correctly forecast a
system’s (process’) future state
Queuing System:
items in queue &
items in service
Arrivals Departures
Queuing System:
items in queue &
items in service
Arrivals
Queuing System:
items in queue &
items in service
Arrivals
λ
L
W
Little’s Law and Arrivals
L = λ W
Average number of
items in a system
Average wait time in
the system for an item
Average arrival rate
Great for:
• Quick “back of the envelope” calculations
• Situations where you have two of the
statistics but measuring the third is
difficult or costly
LL and Arrivals Assumptions
L = λ WAssumptions:
• Stable system (stationary processes)
• Long Running Averages
• Consistent Units
LL and Quick Calculations
L = λ WEXAMPLE
25 weeks2/week *50 bottles
LL and Quick Calculations
L = λ WEXAMPLE
What if we wanted our bottles of
wine to be in the rack longer?
Or for less time?
λTH WCTWIP
But wait…
L = *
CTTHWIP
For departures
Avg work in progress
in a system
Avg cycle time in the
system for an item
Average throughput
(departure rate)
= *
CTWIP =TH *
Maybe this is more familiar?
Queuing System:
items in queue &
items in service
Arrivals Departures
Queuing System:
items in queue &
items in service
Departures
TH
WIP
CT
LITTLE’S LAW ASSUMPTIONS
From which perspective?
Stated in Departures vs. Arrivals?
Looking backward or forward?
Avg Cycle Time =Avg Work In Progress
Avg Throughput
Departures
and
Continuous WIP
#1 -- Consistent Units
Conservation of Flow
For the time period that the calculation
is performed:
#2 -- All work that is started must flow
through to completion and exit the
system
#3 -- Average arrival rate must equal
average departure rate
Time
Cu
mu
lative
Qu
an
tity
WIP
Approx Avg Cycle Time
Cycle Time =Work in Progress
Throughput
Conservation of Flow in Little’s Law
Time
Cu
mu
lative
Qu
an
tity
WIP
Aprx Avg CT
Conservation of Flow in Little’s Law
Stable System?
Stability Part I: Consistent Total WIP
#4 -- The average total Work in
Progress must be roughly
equal at the beginning and at
the end of the time interval for
the Little’s Law calculation
Stability Part II: Average Age of WIP
#5 -- The average age of WIP
should neither be increasing or
decreasing
Examples of Violations of #5:
• Blocked Items
• Items that are allowed to age arbitrarily
• Expedited Items
Little’s Law Defined
Assuming for the time interval of calculation:
1. All measurement units are consistent
2. Average arrival rate = average departure rate
3. All work that enters the system flows through to
completion and exits
4. The average age of WIP is neither increasing
nor decreasing
5. The total amount of WIP is roughly the same at
the beginning and at the end
Avg Cycle Time =Avg WIP
Avg Throughput
So What??
So What??
• The power of Little’s Law is in understanding the assumptions behind what makes it work
• Let the assumptions behind Little’s Law guide your process policies
• By using these policies,
you will be on your way
to predictability
