This paper investigates the application of the Parareal framework to a class of linear dissipative differential equations with a single constant time delay. A direct application of standard Parareal methods to delay differential equations typically results in nonuniform communication patterns due to the exchange of historical data. To overcome this difficulty, we propose a task allocation strategy based on delay intervals, with coarse and fine propagators defined using an implicit time discretization. The full time domain \((0,K\tau ]\) is divided into \(KN\) coarse subintervals of size \(\tau /N\) , with \(N\) subintervals in each delay interval of length \(\tau \) . Fine propagations are performed in parallel using \(P=N\) processors, while the Parareal correction is applied sequentially across successive delay intervals. This strategy localizes the treatment of the delay term and avoids additional data exchange. From a theoretical perspective, we first establish a relationship between the coarse-grid and fine-grid solutions and then derive convergence estimates for the Parareal scheme. The resulting convergence behavior is influenced by the delay structure and stability properties of the propagators. We also define the speedup for an efficiency assessment. Numerical experiments are presented to illustrate the convergence behavior of the method for several examples.
