Queuing Theory : what is the appropriated model when a service can handle more than one client

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For example let's consider a system where we have one Taxi, the Taxi is the service, we don't accept more than 4 clients in the queue, and the Taxi can either take 1 client (with probability 1/2) and 2 clients (with probability 1/2),

In this case, what are the parameters of the queuing system? M/M/1, M/M/1/K ... ?

The problem is that the whole system can hold either 6 clients (4 in the queue and 2 in the Taxi) or 5 clients (4 in the queue and 1 in the Taxi), is it logic? If it is the case, then in this case we have a service that can handle more than 1 client, is it consistent?

Am I missing something?

Thanks in advance,