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This paper studies a large class of M/C/l queues with vacations. By means of a probabilistic interpretation we obtain a functional equation which gives a unified approach to derive time-dependent results for the workload distribution. We also discuss application of our result to a number vacation models. The main results Following Boxma  we consider a modified M/G/1 queueing system which satisfies the following assumptions. 432doi:10.15807/jorsj.38.432 fatcat:5pqpkyvpg5h4poxmoaalh35lbm