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In this paper, we consider the problem of scheduling lightpaths and computing resources for sliding grid demands in WDM networks. Each sliding grid demand is represented by a tuple (v,R,c,p,q,l) , where v is the client node, R is the resource-group which includes a group of predefined resource nodes, c is the required amount of computing resources, [p,q] is the time window and l is the demand duration. With each demand, the scheduling algorithm is required to decide the start time t (p les t les q - l), reserve an amount of c computing resources at a resource node v ' isin R and provision a primary lightpath as well as a backup lightpath from v ' to v . The reserved computing resources and lightpaths are used during [t,t + l]. Unlike the sequential approach wherein the start time, the network resources (lightpaths) and the computing resources are considered one after another, in our work we use the joint scheduling approach wherein the resources and the start time are examined jointly. We consider sliding demands with static and dynamic arrival patterns. We develop an integer linear programming (ILP) formulation to obtain optimal results. For the reason of scalability, we propose heuristic algorithms based on joint resource scheduling and study their effectiveness through simulation experiments.