little's law and predictability - daniel vacanti - agile israel 2014

Little’s Law and

PredictabilityDaniel S. Vacanti

Corporate Kanban

daniel@corporatekanban.com

@danvacanti

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

THANK-YOU!

Daniel S. Vacanti

http://www.corporatekanban.com

daniel@corporatekanban.com

@danvacanti