## 1 Introduction  
In diesel engines, a robust compression-ignited combustion strongly depends on the cylinder charge temperature, composition, and cylinder pressure during valve train events [1]. Variable valve actuation (VVA) technology refers to a technique or combination of technologies that changes valve timing, valve duration, and valve lift, etc., depending on operating conditions and operating strategies, instead of opening and closing intake and exhaust valves with a single, fixed-cam profile. Especially, the compression ignition engine shows the required characteristics of the variable valve system which can control the opening period of the valve. These VVA mechanisms have limited valve lift and timing control, depending on the shape of the mechanism and method in which it is operated. Therefore, it is desirable to design the variable valve operating mechanism in which the ability to control the range of the valve lifting and opening timing is set during the development stage of the actual technology [2]. There are several potential benefits of applying variable valve control to a diesel engine: Optimization of the charge motion, a reduced in-cylinder temperature, and pumping work only if there is no swirl valve, leading to better low-speed performance. Namely, the adoption of the variable valve in a compression ignition engine enables control of the temperature of exhaust gas and effective control of the compression ratio through intake or exhaust air quantity. Based on these functional characteristics, a variable valve system is expected to be essential as a core technology for improving the combustion of diesel engines. The output of the compression ignition engine is affected by the fuel injection system, volume efficiency, friction loss, and pumping loss, etc. Volumetric efficiency depends on the combustion chamber geometry, engine speed, and the timing and lift of valve opening and closing. Therefore, increasing the volumetric efficiency and reducing the loss caused by friction and pumping for the maximum output according to each operating condition improves the power performance. During this optimization process, the optimum intake and exhaust flow rate and timing are adjusted according to the operating conditions without lowering the torque stability and the maximum output [3]. For instance, early exhaust valve opening (EEVO) and cylinder deactivation are implemented to raise the exhaust gas temperatures for DOC activation [4]. In a variable valve strategy known to be effective in controlling the cylinder charge temperature and composition, various exhaust valve mechanisms have been designed to control exhaust gas recirculation (EGR). The term EGR usually refers to a deliberate, external process, but there is also a level of internal EGR. This occurs when the residual combustion gas in the cylinder at the end of the exhaust stroke is mixed with the incoming charge. There is, therefore, a proportion of internal EGR which must be taken into account when planning EGR strategies. Scavenging efficiency will vary with engine load, and in an engine fitted with variable valve timing, a further parameter must be considered. [PERSON] et al. found that internal EGR has a greater potential than external EGR to realize an accurate control of the EGR rate and NOx emission in transient operation [5]. Also, it was found that applying internal EGR moderated combustion by delaying the ignition timing, thereby suppressing in-cylinder pressure oscillations [6]. VVA for automotive diesel engines enables the pre-heating of the exhaust system to be accelerated by the effect of internal EGR [7]. [PERSON] et al. presented a comprehensive scheme to obtain higher exhaust gas temperatures. Internal EGR can be combined with multiple injections after the main injection event, thereby altering the heat release rate and the exothermic reactions in the exhaust stroke [8].