# A Petri Net Model for Cognitive Radio Internet of Things Networks Exploiting GSM Bands +
## 2 Related Works  
A relatively recent paper [21] studied the service time required to transmit a packet in a cognitive radio scenario in the GSM band. The authors considered an exclusive use of the channel by an SU to transmit its packet without allowing spectrum handoff during the transmission. The authors derived the service time distribution of the SUs, taking into account the PU interruptions. The authors considered a time unit for time accounting purposes; these time units were not synchronized with the time slotting process of the GSM time-division multiplexing. Furthermore, the authors assumed that the spectrum sensing was available in the beginning of each time unit and neglected this sensing duration. Although they assumed that their approach could be applicable for a non-null spectrum sensing duration, in this paper, we argue that a synchronization mechanism between the SU and PU is necessary to avoid or reduce disruptive collision generated by the SUs traffic. The authors of [22] focused on the continuous sensing technique to guarantee no interference caused by SUs. An SU continuously senses the channel while transmitting or waiting; it starts its transmission immediately when the channel becomes available and stops it as soon as the PU re-occupies the channel. The SU is able to transmit using different modulation schemes, obtaining a different rate according to the channel condition. The authors modeled the PU behavior by means of a two-state Markov chain, where the transmission slot (the continuous period of time during which the channel is available for SU transmission) and the waiting slot (the continuous time period in between the two transmissions) were modeled as exponential random variables. Moreover, they assumed that the transmission rate can only change in different transmission slots (i.e., it remains unchanged in the same slot). It appears evident that this approach does not accurately match the behavior of a GSM PU, which occupies the channel using slotted periodical multiplexing. In [23; 24], the authors modeled the PU behavior by means of a continuous Markov model while the SU continuously monitored PU activity during transmission; when not transmitting, it was able to adopt a continuous or periodic sensing mode. For both continuous sensing and periodic sensing, the authors obtained analytical results for the probability distribution of the extended delivery time while considering an M/G/1 queuing setup at the SU transmitter. The authors of [25] simultaneously used the TDMA and FDD features of GSM for the first time to enhance the spectrum access performance of CR. They analyzed four different dynamic spectrum access scenarios: (1) when both the PU and BS were outside of the SU transmission range; (2) when only the PU node was located outside of the SU transmission range; (3) when the PU node was within the SU transmission range, while the BS was located outside; and (4) when both the PU and BS were located within the SU transmission range. The authors provided two analytical models when the SUs were near the PU and when the SUs were near the BS to obtain the TDMA channel idleness duration. In the first case, the authors evaluated the available time duration for SU transmission, starting from the probability to have \(p\) PUs inside the area covered by the transmission range of am SU. In the second case, they assumed that the PU packet arrivals followed a Poisson distribution and that the PU packet service time followed an exponential distribution. The GSM primary network was modeled by a finite-state Markov chain, which characterized the state with the number of active PUs in the system. However, the proposed model did not seem to catch the behavior of a typical switching circuit service used in GSM technology [26]. The GSM spectrum availability in Aivero, Portugal was analyzed in [27].