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The article considers a single-channel non-Poisson queuing model GI|G|1|∞ with a FIFO "first-in-first-out" service discipline in stationary conditions and system load intensity less than one. One of the important concepts of the mathematical theory of reliability is the property of increasing the hazard rate (IHR) of homogeneous elements forming reliability systems, otherwise called the aging property. This problem is also of importent for the queuing theory. Two independent in the aggregate and independent of each other sequences: sequence of the waiting times before the start of servicing of actual calls and sequence of the waiting times of virtual calls, starting at time t, or, more precisely, sequence of the durations of the time intervals starting at time t and ending at the moment when the system is free from calls received into the system until time t, are considered. Using the properties of ladder points and ladder heights, as well as applying formulas of Takac's, Cohen's and Hook's, it proved that the widely used in the theory of random walks two above-mentioned sequences of random variables are IHR. [ABSTRACT FROM AUTHOR]

The emergence of peer-to-peer, collective or community self-consumption, and transactive energy concepts gives rise to new configurations of business models for local energy trading among a variety of actors. Much attention has been paid in the academic literature to the transition of the underlying energy system with its macroeconomic market framework. However, fewer contributions focus on the microeconomic aspects of the broad set of involved actors. Even though specific case studies highlight single business models, a comprehensive analysis of emerging business models for the entire set of actors is missing. Following this research gap, this paper conducts a systematic literature review of 135 peer-reviewed journal articles to examine business models of actors operating in local energy markets. From 221 businesses in the reviewed literature, nine macro-actor categories are identified. For each type of market actor, a business model archetype is determined and characterised using the business model canvas. The key elements of each business model archetype are discussed, and areas are highlighted where further research is needed. Finally, this paper outlines the differences of business models for their presence in the three local energy market models. Focusing on the identified customers and partner relationships, this study highlights the key actors per market model and the character of the interactions between market participants. [Display omitted] • Systematic literature review of 135 peer-reviewed journal articles. • Structured analysis with the business model canvas framework from Osterwalder. • Shedding light on emerging business models in markets for local energy trading. • Macro actor categories in P2P, CSC, and TE models are identified and characterised. • Value propositions, key partner and customers and financial structures are discussed. [ABSTRACT FROM AUTHOR]