Call Blocking Probabilities under a Probabilistic Bandwidth Reservation Policy in Mobile Hotspots

In this paper we study a mobility-aware call admission control algorithm in a mobile hotspot. To this end, a vehicle is considered which has an access point with a fixed capacity. The vehicle alternates between stop and moving phases. When the vehicle is in the stop phase, it services new and handover calls by prioritizing them via a probabilistic bandwidth reservation (BR) policy. Based on this policy, new handover calls may enter the reservation space with a predefined probability. When the vehicle is in the moving phase, it services new calls only. In that phase, two different policies are considered: (a) the classical complete sharing (CS) policy, where new calls are accepted in the system whenever there exists available bandwidth, and (b) the probabilistic BR policy. Depending on the selected policy in the moving phase, we propose the probabilistic BR loss model (if the CS policy is selected) and the generalized probabilistic BR loss model (if the probabilistic BR policy is selected). In both stop and moving phases, where the call arrival process is Poisson, calls require a single bandwidth unit in order to be accepted in the system, while the service time is exponentially distributed. To analytically determine call blocking probabilities and the system’s utilization, we propose efficient iterative algorithms based on two-dimensional Markov chains. The accuracy of the proposed algorithms is verified via simulation.

Probabilistic Retry and Threshold Multirate Loss Models for Impatient Calls

In this paper, a link of fixed capacity is considered that services calls from different service-classes. Calls arrive in the link according to a Poisson process, have an initial (peak) bandwidth requirement while their service time is exponentially distributed. We model this system as a multirate loss system and analyze two different multirate loss models. In the first model, named probabilistic retry loss model, if there is no available link bandwidth, a new call is blocked but retries with a lower bandwidth requirement and increased service time. To allow for the fact that a blocked call may be impatient, we assume that it retries with a probability. In the second model, named probabilistic threshold loss model, a call may reduce its bandwidth requirement (before blocking occurs) based on the occupied link bandwidth. To determine call blocking probabilities in both multirate loss models, we show that approximate but recursive formulas do exist that provide quite satisfactory results compared to simulation.

Call-level Analysis of a Two-Link Multirate Loss Model based on a Convolution Algorithm

We consider a two-link system that accommodates Poisson arriving calls from different service-classes and propose a multirate teletraffic loss model for its analysis. Each link has two thresholds, which refer to the number of in-service calls in the link. The lowest threshold, named support threshold, defines up to which point the link can support calls offloaded from the other link. The highest threshold, named offloading threshold, defines the point where the link starts offloading calls to the other link. The adopted bandwidth sharing policy is the complete sharing policy, in which a call can be accepted in a link if there exist enough available bandwidth units. The model does not have a product form solution for the steady state probabilities. However, we propose approximate formulas, based on a convolution algorithm, for the calculation of call blocking probabilities. The accuracy of the formulas is verified through simulation and found to be quite satisfactory.

Congestion Probabilities in Erlang-Engset Multirate Loss Models under the Multiple Fractional Channel Reservation Policy

A communication link that accommodates different service-classes whose calls have different bandwidth requirements and compete for the available bandwidth under the Multiple Fractional Channel Reservation (MFCR) policy is considered. The MFCR policy allows the reservation of real number of channels in order to favor high speed calls. Two call arrival processes are studied: i) the Poisson (random) process and ii) the quasi-random process. In the first case, calls come from an infinite number of sources while in the second case calls are generated by a finite number of sources. To determine call blocking probabilities for Poisson arriving calls, recursive formulas are proposed based on reverse transition rates. To determine time and call congestion probabilities for quasi-random arriving calls, recursive formulas are proven based on the fact that the steady state probabilities cannot be described by a product form solution. The accuracy of the new formulas is verified through simulation.