# A Petri Net Model for Cognitive Radio Internet of Things Networks Exploiting GSM Bands +
## 1 Introduction
Considering the high level of user migration from 2G to 3G/4G and 5G technology, the GSM band shows a lower occupancy level; therefore, it is better suited for a range of CR services [11; 12; 13]. GSM stands for the Global System for Mobile Communications, and it is the world's most popular cellular communications system. As shown in Table 1, GSM operates in various bands. At the beginning of 1997, the European Telecommunications Standards Institute (ETSI) introduced the Enhanced Data Rates for the GSM Evolution (EDGE) to evolve GSM toward third-generation capabilities; starting with the General Packet Radio Service (GPRS) and circuit switched data (CSD), the following enhanced versions were proposed: EGPRS and ECSD. GSM uses a combination of Time-Division and Frequency-Division Multiple Access (TDMA/FDMA). Both the uplink and downlink bands are partitioned in 200 kHz channels. Each channel is divided into eight time slots. Slow frequency hopping can be used to alleviate multipath fading. To reduce interference and battery consumption, GSM devices can make use of power control and discontinuous transmission. Technically, EDGE is primarily a radio interface improvement of GSM/GPRS. The EDGE physical layer parameters appear as almost identical to those of GSM; specifically, the carrier spacing is again 200 kHz, and the TDMA frame structure is unchanged. Although whole channels may be unused at certain times (e.g., at night), a CR device could potentially use unused time slots due to a low-traffic condition or discontinuous transmission. In this case, the approach used by SUs is called the _overlay model_ in contrast to the _underlay model_; in the latter, SUs and PUs can coexist and share the same spectrum with each other by employing Code Division Multiple Access (CDMA), which was used starting from 3G technology, as long as the interference caused by the SUs to PUs is less than the predefined system threshold [14]. The locations of the base stations are usually fixed and depend on the chorography and population density of the specific area. Regardless of this fix positioning of the base stations, one should consider that the mobile operator could decide to switch on a base station in a specific location only for the time length of an event where the presence of a high aggregation of people is expected for a limited time (e.g., a sport event or a live concert). However, mobile locations are not known and often move at a high speed, e.g., in trains or cars, making it difficult for CR devices to avoid interfering with PUs [15]. As in any other packet-switched network, the quality of service (QoS) in a CR network will be affected by three main parameters: throughput (the rate of user data output from a channel averaged over a time interval), time delay (the elapsed time between the instant when the packet arrives at the head of the SU transmitting queue until the instant its transmission ends), and jitter (the range of the time delay over the duration of the communication) [16; 17; 18]. The study of these metrics is particularly important for establishing the QoS in a CRN because they are always affected by the PUs' level of activity [19]. On the other hand, the system complexity makes it rather difficult to derive performance measures through a well established modeling paradigm. We chose Petri nets (PNs) as a modeling paradigm because it is rather natural and simple to represent both parallelism and synchronization with the networks; at the same time, PNs are able to design complex system models in a very easy way through the use of interacting sub-models. This latter feature becomes very important in the context of packet-based wireless systems like the system analyzed here, especially because we want to study the PU behavior when both circuit switching and data packet switching services are implemented in the same base station.