# A Petri Net Model for Cognitive Radio Internet of Things Networks Exploiting GSM Bands +
## 2 Related Works
In this paper, the authors concluded that the distribution of time periods in GSM900 has an exponential behavior and that the GSM900 spectrum is not usable for opportunistic usages due to the high occupancy; in our opinion, these results must be carefully considered because they were obtained in 2011 when the use of 3G was not heavy yet. The traffic and duty cycle patterns in GSM900 in seven different European locations were also analyzed in [28]. The authors performed synchronized measurements and pointed out that the actual activity patterns can have significant variations. Accordingly, the design of secondary users should avoid a simplified assumption of the traffic patterns. The authors of [29] performed a similar work in India, considering four different scenarios (both outdoor and indoor). Specifically, they measured a spectrum occupancy for a GSM900 no greater than 10% in uplink and between 86% and 97% in downlink. Ref. [30] is one of the most recent works that addresses the problem of identifying the GSM signal. Using the Kolmogorov-Smirnov test as a decision criteria, the authors performed an identification using the magnitude of the observed signal samples in terms of its cumulative distribution function. They obtained an identification score of approximately 100% with an observation period of 200 us using both an AWGN channel with an SNR equal to 2 dB and a ITU-T pedestrian A fading channel with an SNR equal to 15 dB. With this fast identification, SUs could be able to use one half of each time slot when PUs are identified as inactive. A demo implementing spectrum sensing and interaction with GSM BSs using SDR devices has been presented in [31]. Moreover, in [19; 32], the spectrum sensing was performed using an SDR device; specifically, it was a Universal Software Radio Peripheral (USRP) model B100 device manufactured by Ettus Research. The authors used the spectrum sensing procedure in order to characterize the periods of time when the channel was used by the GSM radio system and to validate their theoretical model for the distribution of SUs packet service delivery time. Since their introduction in the [PERSON]'s seminal work [33], Petri nets have been widely used for representing a large number of systems in very different fields, such as computer engineering, biology, economy, and telecommunications. Their use in telecommunication systems is quite relevant thanks to their ability to model parallelism and synchronizations together with time delay-characterizing events; thus, they are capable of effectively studying telecommunication infrastructure performances. Many Petri net extensions have been proposed and used over time in order to represent different timings and complex behaviors. Generalized stochastic Petri nets (GSPNs), deterministic and stochastic Petri nets (DSPNs), and fluid stochastic Petri nets (FNSPs) have been exploited in [34] for the study of wireless Internet access systems based on GSM/GPRS technology; the authors' purpose was to compare the three Petri net approaches to find the most effective one for estimating the performance indices of realistic configurations of GSM/GPRS systems. The evaluated metrics considered in [34] were radio and voice block probabilities and the average number of radio blocks in the base station buffer. The sub-model we propose here is instead designed for evaluating the probability that a slot in the frame is busy because of either a voice call or a data transmission that is in progress because of a PU. As detailed in Section 4.2, these latter probabilities are used in the SU model for deriving SU QoS metrics. Petri net extensions are also used in [35], where the authors focused on the resiliency of 5G telecommunication networks. Ref. [35] shows how Petri net-based methodologies can be profitably exploited in support of telecommunication network designs despite their complexity. An availability model of 5G networks was proposed, and the system was analyzed at different levels: physical infrastructure, virtual infrastructure, and network services.