Problem $1-($Queue network$)$ Axa An insurance company receives insurance claims on a random basis. Statistics suggest that an average of $23$ claims have been received per hour. Claims are screened first to be classified as either Easy or Hard claims. Work sampling approach has estimated the average screening time of the claims is $15$ min. Historical data suggest that after screening, an average of $8$ claims are Easy ones and the remaining $15$ ones are considered as Hard claims. Easy claims are processed which takes an average of $15$ minutes each, after which the Easy claims are approved by the Management office for $12$ min each. The Hard claims are processed for an average time of $30$ min each, then reviewed for an average of $20$ minutes each and finally approved by the same aforementioned Management office for the same $12$ min each as above. The arrival of the claims to the company and the service durations are random variables and Markovian $($i$.$e$.$ Poisson arrival rates and $[$negative$]$ exponential service times$).$ The claims are stacked $($lined up$)$ on a First Come First Serve basis $($FCFS policy$)$ between every two consecutive operations, waiting to go through. $1.$ Draw the corresponding que network. $2.$ Identify the minimum number of officers$/$clerks at each stage$/$operation in order to maintain system$/$network stability $($Underloaded$)3.$ Calculate the Wq for each of the stages$/$operations for each type of the claims and show them on your network. $4.$ What would be the overall average Wait time in the system $($Ws$)$ for Easy claims as well as for Hard claims. $5.$ If a customer asks you how long an insurance claim filed by her, would roughly take to be handled by the company, what would you honestly tell her? You have to give one number.