Heuristics for scheduling data gathering with limited base station memory

Abstract

In this paper, we analyze scheduling in data gathering networks with limited base station memory. The network nodes hold datasets that have to be gathered and processed by a single base station. A dataset transfer can only start if sufficient amount of memory is available at the base station. As soon as a node starts sending a dataset, the base station allocates a block of memory of corresponding size. The memory is released when computations on the dataset finish. We prove that minimizing the total data gathering and processing time is strongly NP-hard. As this problem is a special case of a specific resource constrained flow shop scheduling problem, for which an exact exponential algorithm is known, we propose several simple polynomial-time heuristics and two groups of local search algorithms, and test their performance in computational experiments. We show that the local search algorithms produce very good schedules, and one of the simple heuristics delivers solutions of comparable quality in a very short time.

Two-machine flow shop with dynamic storage space

“…Consider the following instance of the decision version of the makespan minimisation problem F2|storage, ω j , Ω(t), p i, j = 1|C max : Observe that this instance satisfies the condition (1) and suppose that there exists a schedule σ with the makespan that does not exceed 3r , i.e. assume that the answer to the scheduling problem is YES.…”

“…assume that the answer to the considered instance of NMTS is YES. Then, the schedule where, for each job g, S 1 g + 1 = S 2 g and where, for each 1 ≤ k ≤ r , S 1 i k = 3(k − 1) and S 1 j k +r = 3k − 2, has the required makespan of 3r .…”

“…If ω j 1 < 6, then at least one unit of the resource is wasted in the interval [0, 1), and at least one unit is lost in the interval [1,2). Thus, ω j 1 = 6, j 1 = 1, and this job completes on M 2 at time C 2 1 = 2, as otherwise at least 6 units of the resource would be wasted in the interval [1,2). Similarly, let j 2 be the second job in σ .…”

“…A number of applications, ranging from multimedia systems [14] and star data gathering networks [1] to supply chains of mineral resources [7], motivated the recent interest in the two-machine flow shop with limited storage space, also referred to as the two-machine flow shop with job dependent buffer requirements. This direction of research focuses on the situations with two distinct characteristics: (1) each job requires some storage space and the storage requirements vary from job to job; and (2) each job seizes the required portion of the storage space (buffer) from the start of its first operation till the completion of its second operation.…”

Scheduling in data gathering networks with background communications

“…Berlińska (2014) analyzed maximizing the lifetime of a network with limited memory of nodes acquiring the data. Algorithms minimizing data gathering time were proposed for networks with data compression (Berlińska 2015;Luo et al 2018a, b) and networks with limited base station memory (Berlińska 2020). Minimizing the maximum dataset lateness was studied by Berlińska (2018a).…”