4.10. Consider the five-processor system described in Conceptual Problem 4.3.

Suppose that the system maintenance starts as soon as the system crashes. The

amount of time needed to repair the system is an Exp(lambda) random variable, at the

end of which all five processors are functioning. Model this system as a CTMC.

Using

4.3. A computer has five processing units (PUs). The lifetimes of the PUs are iid

Exp(mu) random variables.When a PU fails, the computer tries to isolate it automatically

and reconfigure the system using the remaining PUs. However, this process

succeeds with probability c, called the coverage factor. If the reconfiguring succeeds,

the system continues with one less PU. If the process fails, the entire system

crashes. Assume that the reconfiguring process is instantaneous and that once the

system crashes it stays down forever. Let X(t) be 0 if the system is down at time t ;

otherwise it equals the number of working PUs at time t . Model {X(t); t >= 0} as a

CTMC, and show its rate matrix.

Here's the question from the textbook (I'm trying to insert pictures but they just disappear, so here's a drive link to the pics):

https://drive.google.com/open?id=1Pm5lK3gDUhwZHVVRdMcDl2-fMi15w-hh

4.10. Consider the five-processor system described in Conceptual Problem 4.3. Suppose that the system maintenance starts as soon as the system crashes. The amount of time needed to repair the system is an Exp (2) random variable, at the end of which all five processors are functioning. Model this system as a CTMC. additional information needed: 4.3. A computer has five processing units (PUs). The lifetimes of the PUs are iid Exp() random variables. When a PU fails, the computer tries to isolate it automat- ically and reconfigure the system using the remaining PUs. However, this process succeeds with probability c, called the coverage factor. If the reconfiguring suc- ceeds, the system continues with one less PU. If the process fails, the entire system crashes. Assume that the reconfiguring process is instantaneous and that once the system crashes it stays down forever. Let X(/) be 0 if the system is down at time /; otherwise it equals the number of working PUs at time /. Model {X(/),/ 2 0; as a CTMC, and show its rate matrix