# An Analytical Framework in OFDM Wireless Networks Servicing Random or Quasi-Random Traffic
## 1 Introduction  
The determination and evaluation of the main quality of service (QoS) parameters, such as call blocking probabilities (CBP) and network resources utilization, is a complex task in contemporary networks, due to the growth of network traffic and the high traffic stream diversity [1]. The latter necessitates research on teletraffic loss or queueing models, either at call-level or at packet-level [2; 3; 4; 5; 6; 7]. Such models not only assist in network optimization and dimensioning procedures but they may also be used in combination with machine learning techniques [8; 9] or as an input to computational intelligent techniques, such as the fuzzy analytical hierarchy process techniques [10; 11]. In this paper, we concentrate on call-level teletraffic loss models. The simplest call-level loss models adopt as a call arrival process the classical Poisson process, which leads to analytically tractable formulas for the determination of performance measures, such as CBP and resources utilization. The origination of calls in the Poisson process results from an infinite number of users (or traffic sources). This means that the Poisson process cannot capture the case of calls generated via a finite number of users. The latter can be well described by the quasi-randomarrival process. This call arrival process depends on the number of idle users (that are capable of generating traffic) and is smoother than the Poisson process. Because of this, the CBP in a system that carries quasi-random traffic are much lower compared to the corresponding CBP of a system that carries random (Poisson) traffic. For recent applications of the quasi-random process in loss systems, the interested reader may resort to [12; 13; 14; 15; 16]. We consider the cases of random and quasi-random traffic in the downlink of an orthogonal frequency division multiplexing (OFDM)-based cell which provides service to calls from many service-classes. OFDM is a dominant technology in 4 th generation (4G) networks and can also be considered as a candidate technology in 5 th generation (5G) networks [17; 18; 19; 20; 21] and in cognitive radio networks [22]. The analysis of this OFDM-based cell relies on the loss models of [23; 24; 25; 26]. The case of a batch arrival process and two types of calls, narrow-band and wide-band, has been studied in [27] under two different batch blocking disciplines: (a) the complete and (b) the partial batch blocking discipline. A possible extension of [27] that may result in efficient formulas for the CBP determination can be based on the works of [28; 29; 30] (for the partial batch blocking discipline) and [31] (for the complete batch blocking discipline). In [23], [PERSON] and [PERSON] (P-S) consider an OFDM-based cell that accommodates different service-classes whose calls follow a Poisson process. The P-S system is described as a loss system, i.e., calls are blocked and lost in the case of resource unavailability. This means that the adopted policy for resource sharing in [23] is the complete sharing (CS) policy. The CS policy is the default policy in teletraffic loss models, but it may result in an unfair resource allocation among calls [1; 2]. Contrary to [24; 25], where a new call is accepted in the OFDM-based cell only if the required subcarriers are available, in the P-S model the admission of a new call is based on the availability of both subcarriers and power. Apart from this significant modification in the call admission, it is important to mention that the model of [23] has a product form solution (PFS) for the steady-state probabilities. The existence of a PFS is significant in loss/queueing models, since it results in efficient algorithms (of recursive or convolutional form) for the performance measures calculation [32; 33; 34; 35; 36; 37]. However, in the P-S model, the calculation of CBP and resource utilization is based on complicated algorithms which are unattractive for network planning engineers.