In recent years, there has been significant advancement in resource management mechanisms for cloud~computing infrastructure performance in terms of cost, quality of service (QoS) and energy consumption. The emergence of the Internet of Things has led to the development of infrastructure that extends beyond centralised data centers from the cloud to the edge, the so-called cloud-to-thing continuum (C2T). This infrastructure is characterised by extreme heterogeneity, geographic distribution, and complexity, where the key performance indicators (KPIs) for the traditional model of cloud~computing may no longer apply in the same way. Existing resource management mechanisms may not be suitable for such complex environments and therefore require thorough testing, validation and evaluation before even being considered for live system implementation. Similarly, previously discounted resource management proposals may be more relevant and worthy of revisiting. Simulation is a widely used technique in the development and evaluation of resource management mechanisms for cloud~computing but is a relatively nascent research area for new C2T~computing paradigms such as fog and edge~computing. We present a methodical literature analysis of C2T resource management research using simulation software tools to assist researchers in identifying suitable methods, algorithms, and simulation approaches for future research. We analyse 35 research articles from a total collection of 317 journal articles published from January 2009 to March 2019. We present our descriptive and synthetic analysis from a variety of perspectives including resource management, C2T layer, and simulation.