With the prevalence of technology and computer systems in today’s society, it is crucial to ensure that the systems we use are secure. The fields that study these issues, cybersecurity and cybersafety, use the formal verification technique of modelchecking. This paper tackles one aspect of the work needed to develop model-checking methods as we try to improve the efficiency and the reliability of model-checking techniques using the Time Petri Net model. Formal methods based on Time Petri Nets are not exempt from the state-explosion problem, and we study here different approaches to circumvent this problem. In particular, we show that limiting the exploration of such a model to runs with integer dates maintains the integrity of the model-checking result. We also show that it is possible to set a limit on the number of runs that can be explored while maintaining the probability that the observation is correct above a certain threshold. / Med tanke på hur vanligt det är med teknik och datorsystem i dagens samhälle är det viktigt att se till att de system vi använder är säkra. De områden som studerar dessa frågor, cybersäkerhet och cybersafety, använder den formella verifieringstekniken modellkontroll. Denna artikel tar upp en aspekt av det arbete som krävs för att utveckla metoder för modellkontroll, eftersom vi försöker förbättra effektiviteten och tillförlitligheten hos metoder för modellkontroll med hjälp av Time Petri Netmodellen. Formella metoder baserade på Time Petri Nets är inte undantagna från problemet med tillståndsexplosion, och vi studerar här olika tillvägagångssätt för att kringgå detta problem. I synnerhet visar vi att om man begränsar utforskningen av en sådan modell till körningar med heltalsdatum bibehålls integriteten hos resultatet av modellkontrollen. Vi visar också att det är möjligt att sätta en gräns för antalet körningar som kan utforskas samtidigt som sannolikheten för att observationen är korrekt hålls över ett visst tröskelvärde.

Call centers have become a preferred and prevalent means for companies to communicate with their customers. As a consequence of this, the call center industry has seen a huge growth in both volume and scope in the last couple of decades. Operations managers are challenged with the fact that personnel costs, especially staffing, account for over 65% of the cost of running the typical call center. The trade-off between service quality (marketing) and efficiency (operations), thus naturally arises, and a central goal of ours is to contribute to its understanding. We present here a server switching policy for routing of calls to Customer Service Representatives (CSR) in a multi-skilled inbound call center utilizing skill-based routing (SBR). We model the system as a queueing network and propose stochastic Petri net based models for the design and performance analysis of call centers. Our models and experimentations help in identifying practices that result in efficient usage of existing personnel in a call center. In our work, we have considered two types of scenarios in which a multi-skilled SBR call center handling inbound calls can function - (i) with specialist agents only, and (ii) with a mix of specialist and flexible agents. We have developed both these models and compared the rewards obtained from each of them. This analysis helped us answer important issues regarding the routing decision of calls to CSRs, identify the hedging point where one obtains the highest rewards and the impact of varying the strategic and tactical level decisions on the overall call center performance.

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