Consider a three-tiered system interfacing to a centralized DBMS, in which n1 presentation servers are connected to n2 application servers, which in turn are connected to n3 transaction servers. Assume that for each transaction, the application server, on average, invokes k procedures, each of which is executed on an arbitrary transaction server, and that each procedure, on average, executes s SQL statements that must be processed by the DBMS. If, on average, a presentation server handles r requests per second (each request produces exactly one transaction at the application server), howmany SQL statements per second are processed by the DBMS and how many messages flowover each communication line?

What will be an ideal response?

r ? n1 ? k ? s statements per second are processed by the DBMS.
Each line connecting a presentation server to an application server handles 2 ? r messages per second
Each application server is connected to n1/n2 presentation servers and therefore invokes r ? k ? (n1/n2) procedures per sec. Assuming that an application server is connected to all transaction servers and that it randomly chooses a transaction server to execute a procedure, the number of invocations over a particular line connecting the application server to a transaction server is r ? k ? (n1/n2)/n3, and hence the number of messages over the line is twice that number.
The number of statements transmitted over a line connecting a transaction server to the DBMS is r ? n1 ? k ? s/n3, and hence the number of messages over the line is twice that number.