Markovins Chain Model

Example• Hari, a persistent salesman, calls ABC Hardware Store once a week

hoping to speak with the store's buying agent, Shyam. If Shyam does not accept Hari's call this week, the probability he will do the same next week (and not accept his call) is .35. On the other hand, if he accepts Hari's call this week, the probability he will not accept his call next week is .20.

Example: Transition Matrix

Refuses Accepts

Refuses .35 .65

Accepts .20 .80This Week’s

Call

Next Week’s Call

Example• How many times per year can Hari expect to talk to Shyam?• Answer: To find the expected number of accepted calls per year, find

the long-run proportion (probability) of a call being accepted and multiply it by 52 weeks.

ExampleLet 1 = long run proportion of refused calls 2 = long run proportion of accepted calls

Then,

.35 .65

[1 2 ] .20 .80 = [1 2 ]

Example + = (1) + = (2) + = 1 (3)

Solve for and

• The probability of the system being in a particular state after a large number of stages is called a steady-state probability.