Abstract: It is a complicated problem in queue networks to optimally control the delay and service rate．For multi-class priority queue and adjustable service rate M/G/1queues,two convex optimization problems were studied,i.e.,minimizing convex functions of the average delay vector,and minimizing average service cost,both under the constraints of per-class delay,and consiquently an optimization algorithm was proposed for each of them．These algorithms use virtual queue techniques to solve the two problems with variants of dynamic cμ rules．Then these algorithms adaptively choose a strictly priority policy,in response to past observed delays in all job classes,in every busy period．Lyapunov drift analy-sis and simulation results validate the optimal performance of these two algorithms,and show that the proposed polices require limited or no statics of the queue.

Key words: Multi-class priority,Service rate,Priority policy,Delay