# Simple circuit-switched network

I'm having a problem understanding this question regarding circuit-switched networks. I get the main concept that the connections are reserved for each link, but these two questions are confusing me. I was asked to find two things:

1. The maximum number of simultaneous connections that can be in progress at any one time.
2. The maximum number of simultaneous connections that can be in progress at any one time if all the connections are between the switch in the upper-left-hand corner and the switch in the lower-right-had corner.

I'm not sure about the first question (my guess is 4 connections), but I'm pretty positive that the answer for the second question is 4 connections. I'm not asking for an answer. I'm just trying to understand the difference between the two questions. Thanks for the help.

Solution for question 2:

• It does not seem very technical if all you can work with is picture without any descriptions (are we limited by the amount of computers shown, the amount of 'unconnected' links from devices or amount of connections between devices? Is single connection bidir or unidir, are links full or half duplex? Can links be multiplexed somehow? etc) I would randomly guess 16 and 8. You probably have lot more context in the source material you're going through and probably should be able to find the answer with minimal work.
– ytti
Sep 7 '13 at 15:23
• I really tried to understand the questions but I just don't get it. Here is what the textbook says: "In this network, the four circuit switches are interconnected by four links. Each of these links has four circuits, so that each link can support four simultaneous connections. The hosts are each directly connected to one of the switches. When two hosts want to communicate, the network establishes a dedicated end-to-end connection between the two hosts." How is that possible that each link can support four simultaneous connections?
– user2592
Sep 7 '13 at 17:23
• @wizardo There are a number of ways. In modern systems, you'd be using some sort of multiplexing, such as time-division multiplexing (alternating sending some block from each circuit, like in ATM or T-carrier networks) or frequency-division multiplexing (like in cable television or optical fiber with multiple wavelengths). In a simpler system, you might have a bundle of wires, and each pair of wires carries one connection (think multi-conductor speaker cable). Sep 7 '13 at 17:59

Circuit-switched networks have to reserve a segment for each hop along the journey, so the farther away the two connected endpoints are, the more links are reserved for the call. In your case, if the upper-left router were making calls to the lower-left router, only the segments on the left side of the diagram were being in use, while all the others were still free, but as shown, when it calls the lower-right router, it has to use segments from two of the sides to get there.

You can fit a lot more calls in if each call just needs one hope than if each call needs multiple.

• but... the OP asked about some numerical calculations... Sep 7 '13 at 19:11
• @MikePennington He was asking about the difference between the two questions, and the essence of the difference is in the requirement to reserve segments all along the path. Sep 7 '13 at 19:12
• @chrylis: So from what I understand, the answer for the first question is 16 connections, and the second question is 12.
– user2592
Sep 7 '13 at 19:44
• @wizardo The first part is correct. For the second part, try actually highlighting lines to represent opening connections and see how many lines you can draw from UR to LL. Sep 7 '13 at 19:49
• @chrylis: I think I got it. It's 8, right? (I posted an image in the question section.)
– user2592
Sep 7 '13 at 20:25