# Call Blocking Probabilities under a Probabilistic Bandwidth Reservation Policy in Mobile Hotspots
## 1 Introduction  
Call admission control (CAC) is a significant quality of service (QoS) mechanism in contemporary networks, not only because it controls the access to the bandwidth units (b.u.) required by new mobile users but also because it provides fairness among different mobile applications and at the same time affects the QoS of in-service calls [1, 2, 3, 4]. Considering call-level traffic in wireless networks, such a QoS mechanism is a resource sharing policy that affects call blocking probabilities (CBP) of both new and handover calls. The term CBP refers to the blocking of new or handover calls due to the unavailability of b.u. To reduce CBP (especially of handover calls), various bandwidth sharing policies exist in the literature, with the most common being the guard channel or bandwidth reservation (BR) policy [5, 6, 7, 8, 9, 10, 11, 12]. The main characteristic of the BR policy is that it introduces a priority to handover calls by reserving b.u. in favor of them. On the other hand, such a reservation usually results in a significant CBP increase of new calls [13, 14, 15, 16]. We focus on a CAC mechanism proposed in [7] that is based on the BR policy and is applied on a mobile hotspot. The work of [7] considers a vehicle that has an access point (AP) installed on it with a wireless local area network (WLAN) capacity of \(C\) b.u. The vehicle can be in two different phases: (a) in the stop phase and (b) in the moving phase. During the stop phase, a vehicle remains in a location (e.g., a station area) and can accommodate two different types of users: new and handover users. New users may initiate a call when they enter the vehicle. On the other hand, handover users have anongoing call and perform a handover from a NodeB (NB) to the vehicle's AP. To favor handover users, in terms of reduced CBP, a part of the C b.u. is reserved for them. During the moving phase, only new calls can be generated. To this end, two policies have been studied in that phase. They are: (i) the classical complete sharing (CS) policy, where b.u. are provided to a new call if they exist at the time of the call's arrival, and (ii) the BR policy, where a part of the \(C\) b.u. cannot be accessed by new calls (although handover calls are not generated during the moving phase), a fact that substantially increases the CBP of new calls. In both phases, calls require a single b.u., follow a Poisson process and have an exponentially distributed service time. The main target of [7] is the CBP determination in the stop and moving phases, as well as the computation of the system's utilization with the aid of a 2-D Markov chain analysis. The reason behind the usage of a two-dimensional Markov chain lies in the fact that two phases (the stop and the moving) exist in the model and interact with each other. A model similar to [7] has been proposed in [6] and recently improved in [17]. In [6, 17], the stop and moving phases are treated independently. Such a fact simplifies the corresponding Markov chains as well as the necessary analytical CBP calculations (which are based on the classical Erlang B formula [18, 19]), but may lead to analytical CBP results that are not always close to the corresponding simulation results. The idea of the stop-moving phases may also be considered for the CBP determination in the more demanding framework of high-speed railway communications, but this is still an open research issue [20, 21, 22]. In this paper, we extend the work of [7] by proposing a probabilistic BR policy that can be applied to new calls (either in the stop or in the moving phase) with a predefined probability that can be different for each phase. The reason behind studying such a probabilistic BR policy is the following: when the \"strict\" BR policy is applied to prioritize a certain type of call, it can lead to a substantial CBP increase in other types of calls that share the same b.u. [17, 18, 19, 23, 24].