Suppose thot a network switch center has n 3 slots to accommodate incoming high and low' priority clients, with arrival ratca of 3 and At and departure rates of yt and , respectively. A high priority client must alweys ocrupy one Bill slot. A low priority rlient, on the other hand, car lower its quality of service (QoS) by occupying only one half of a slot, if necessary. \V1ieu a low priority client occupies a full slot. we cell it a low priority, high Qob client : when it oecupim one held of a slot. we call it a low prioriy, low QoS client. Draw a Markov state transition diagram for modeling the following resource control policy:

2. If there is at least one full slot avsileble, an incoming client always occupies an empty full slot, regardless of ita priority class.
4. IN cede (i) is not true, en incoming high priority client can lower the JS of two low priority, high QJ clients, if they are available, after which the high priority client occupies one full slot and the two low pricirity, high QoS clients liutb liecume low pricirity, luw QoS clients, with eanli occupying one half nlot.
6. If case (i) is not true, ar incoming low priority' client cen lever the QoS of one low priority, high QoS client, if it is available, after which each occupies one half slot.
8. A rient will turn away if nine f the ahive. :asm is app1i:ahle.
10. A low priority, low QoS client occupying one half slot can immediately become e low priority, high QoS client occupying one full slot upon a client s departure.

Use the representation (o. 6, c) where o stands for the number of low-priority, low QoS clients. 6 stands for the niimher of liw-priority, high QiiS i:liemts, and r tide for the number ref high-priirity i:mentn. Organize the Llarkov model to that when e high priority client arrives, the transition goes right, and when a low' priority climit arrives, the tr it ion goes down. Lablc tLc transition rate of cach trmnitiou clearly. Ana time g = /i3 = 3 and = = 4. Use Sharpe and essign rewards to states of the Merkov model to obtain:

(a) the averepe number of low-priority clients (regardless of their QA levels) in the system;