Computer Networking: A top down approach on TDM (need help understanding this)

Question

Consider a switch that uses time division multiplexing (rather than statistical multiplexing) to share a link between four concurrent connections (A, B, C, and D) whose packets arrive in bursts. The link’s data rate is 1 packet per time slot. Assume that the switch runs for a very long time. The average packet arrival rates of the four connections (A through D), in packets per time slot, are 0.2, 0.1, 0.2, and 0.1 respectively. The average delays observed at the switch (in time slots) are 10, 5, 10, and 5. What are the average queue lengths of the four queues (A through D) at the switch?

Here is how i see the problem I understand from Time division multiplexing that access to the shared link is provided to each connected device(A,B,C and D) at regular time intervals/slots. When it says that the link's data rate is 1 packet per time slot, does it mean that it is this speed for one time slot which is further divided into 4 slots, thus the data rate for each slot effectively being 0.25 packets per time slot. Or does it mean that it is 1 packet per time slot for each slot that is available to each device.

For now, lets consider that it is essentially 0.25 packets per time slot.

Further 0.2,0.1,0.2 and 0.1 packets arrive per time slot for each device(the exact rate may vary as the packet arrive in bursts but for calculations average will do).

Now, how i see this is that as the control transfers from A->B->C->D(4 slots), the packets from A continue to arrive at the rate of 0.2 packets per slot, i.e during the slot when A has the access to the shared link, and even when B,C and D have access, packets from A continue to arrive at 0.2 packets per second. When packets from A are given access to the shared link, for the first time, the input is at an average of 0.2 while the outgoing is at an average of 0.25 thus the packets are transferred successfully, i.e without any delay, but when the control circulates to A for the second time, 0.6 packets would already have accumulated for it. So 0.25 being less would never be able to compete and the queue would continue to grow unbounded. What is the correct way to view this problem?

• Caleb Stanford: Hello! It might help to ask a more specific question. Not just, I need more help understanding all of this & how to view it, etc.