In edge computing, edge devices can offload their overloaded computing tasks to an edge server. This can give full play to an edge server’s advantages in computing and storage, and efficiently execute computing tasks. However, if they together offload all the overloaded computing tasks to an edge server, it can be overloaded, thereby resulting in the high processing delay of many computing tasks and unexpectedly high energy consumption. On the other hand, the resources in idle edge devices may be wasted and resource-rich cloud centers may be underutilized. Therefore, it is essential to explore a computing task collaborative scheduling mechanism with an edge server, a cloud center and edge devices according to task characteristics, optimization objectives and system status. It can help one realize efficient collaborative scheduling and precise execution of all computing tasks. This work analyzes and summarizes the edge computing scenarios in an edge computing paradigm. It then classifies the computing tasks in edge computing scenarios. Next, it formulates the optimization problem of computation offloading for an edge computing system. According to the problem formulation, the collaborative scheduling methods of computing tasks are then reviewed. Finally, future research issues for advanced collaborative scheduling in the context of edge computing are indicated.

The subject matter of the article is the working-chamber geometry and the isentropic performance of the two-apex (m = 2) Wankel rotary compressor ‒ a two-apex rotor orbiting within a single-lobe peritrochoid housing at a 2:1 eccentric-shaft gear ratio ‒ a configuration geometrically well suited to gas compression yet, unlike the classical three-apex (m = 3) engine, it is almost unstudied analytically. The goal is to derive, rigorously and from first principles, the complete set of closed-form geometric and performance relations of the m=2 machine, exact expressions for which have not previously appeared in the literature, and to render the exact profiles manufacturable. The tasks to be addressed are: to establish the kinematics and the 2:1 synchronizing-gear relation; to derive the exact housing and rotor (envelope) profiles together with the working-chamber area and volume laws; to obtain the displacement, compression ratio and apex-seal oscillation limit in closed form; to construct manufacturable profiles that decouple the running clearance from the shape factor; and to develop the asymptotic scaling laws, the closed-form isentropic performance, and a design equation relating the ideal gain with any loss model. The methods used are: the differential geometry of trochoidal envelopes, Green's theorem for the chamber area and volume, the Taylor (asymptotic) expansion of the governing shape function, and closed-form isentropic thermodynamic analysis. The following results were obtained: the working-chamber volume law , with and shape factor , together with its exact crank-angle rate; exact theorems for the displacement (about larger than for at identical e, R, b), the compression ratio , and the apex-seal law giving versus 6 for m = 3; exact normal parallel-offset profiles decoupling the running clearance from K, removing the principal obstacle to precise CNC manufacture in earlier circular-arc treatments; four asymptotic design laws from a single expansion of — , (within 1.3 % for K ≥ 4), (1 % clearance already at , no dead-volume machining), and volumetric-compactness advantage over m = 3 at the respective kinematic limits; and the isentropic indicated work in closed form, , yielding and a strict monotonicity theorem. Conclusions. The scientific novelty of the results obtained is as follows: 1) for the first time the complete exact closed-form geometry of the Wankel compressor was derived from first principles, rigorously quantifying its advantages over m = 3; 2) the exact normal parallel-offset method was developed, decoupling running clearance from shape factor and rendering the exact profile directly CNC-manufacturable, overcoming the chief limitation of earlier circular-arc practice; 3) the closed-form isentropic performance and the design equation were obtained, separating the analytically known ideal gain from any loss model and providing a verified geometric and performance basis for subsequent thermodynamic and loss analysis.