Dynamic Scheduling with Convex Delay Costs: The Generalized $c|mu$ Rule

Dynamic Scheduling with Convex Delay Costs: The Generalized c Rule

We consider a general single-server multiclass queueing system that incurs a delay cost Ck( k) for each class k job that resides k units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a nite time horizon. Denote the marginal delay cost and (instantaneous) service rate functions of class k by ck = C 0 k...

Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cµ-Rule

We consider a queueing system with multitype customers and flexible (multiskilled) servers that work in parallel. If Qi is the queue length of type i customers, this queue incurs cost at the rate of Ci Qi , where Ci · is increasing and convex. We analyze the system in heavy traffic (Harrison and Lopez 1999) and show that a very simple generalized c -rule (Van Mieghem 1995) minimizes both instan...

Online companion for Scheduling Flexible Servers with Convex Delay Costs In Many-Server Service Systems

Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems

I a recent paper we introduced the queue-and-idleness ratio (QIR) family of routing rules for many-server service systems with multiple customer classes and server pools. A newly available server serves the customer from the head of the queue of the class (from among those the server is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fa...

The single-server scheduling problem with convex costs

Being probably one of the oldest decision problems in queuing theory, the single-server scheduling problem continues to be a challenging one. The original formulations considered linear costs, and the resulting policy is puzzling in many ways. The main one is that, either for preemptive or nonpreemptive problems, it results in a priority ordering of the different classes of customers being serv...