Question

A community is served by two cab companies. Each company owns two cabs and both share the
market equally, as evidenced by the fact calls for service arrive at each company’s dispatching office
at the rate of eight per hour. The average time per ride is 12 minutes. The two companies were
recently bought by an investor, who is interested in consolidating them into a single dispatching
office. Is that beneficial to the community (assuming that pricing stays the same)?

Answer 1

Now let's compare both the models:

		Lambda	mu	c	System/Source Limit
Model 1	M/M/2	8 calls per hour	5 rides per cab per hour	2	Infinite
Model 2	M/M/4	16 calls per hour	5 rides per cab per hour	4	Infinite

Let's compare both the models on the basis of how much a customer has to wait for a ride on an average. We can calculate Wq from the formula or from TORA.

Wq for the two-cab situation = 0.356 = 21 minutes

Wq for the consolidated single dispatching office = 0.149 = 9 minutes

Hence, a customer has to wait less and hence it is beneficial for the community.