Traffic analysis of heterogeneous mobile cellular networks using “wrap-up” cell structure

In this paper, we develop a tool for evaluating performance of a heterogeneous mobile network under different traffic conditions. The traffic condition is specified in a cluster of seven heterogeneous base stations, and “wrap-up” cell structure is applied to account for the traffic that crosses the boundary of the cluster. The performance of the network is specified in metrics which can be computed using the algorithm developed. These metrics relate to call rejection, i.e. the blocking of new calls, and the termination of handoff calls, as well as the carried traffic i.e. the expected number of ongoing calls in a station. These metrics are either measured for a single base station in a cluster, or measured for the average over the whole cluster. We apply the algorithm to some hypothetical data and present the numerical results. We also consider approximating a heterogeneous model with a simpler homogeneous model. Through some numerical results, we demonstrate the magnitude of errors that could result in the approximation.     

Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation

In this paper, Radial Basis Function (RBF) method for interpolating two dimensional functions with localized features defined on irregular domain is presented. RBF points located inside the domain and on its boundary are chosen such that they are the image of conformally mapped points on concentric circles on a unit disk. On the disk, a fast RBF solver to compute RBF coefficients developed by Karageorghis et al. (Appl. Numer. Math. 57(3):304–319, 2007) is used. Approximation values at desired points in the domain can be computed through the process of conformal transplantation. Some numerical experiments are given in a style of a tutorial and MATLAB code that solves RBF coefficients using up to 100,000 RBF points is provided.     

A discrete time-limited vacation model for the fair share scheduler

We present a vacation model which can be used as a component of the type of polling system encountered in a fair share scheduler. Consider two queues in tandem attended by one server. The primary queue Q _p, which has an infinite buffer, has a preemptive priority over the secondary queue Q _s which has a finite buffer. Jobs which complete service at the primary queue will go into the secondary queue for another service with a probability p. The server visits Q _s for a maximum of T units of time. After visiting for T units of time or after Q _s becomes empty, whichever occurs first, the server goes on a vacation. The duration of this vacation has a phase type distribution. The vacation can also be interrupted in order to attend to the jobs in Q _p. The resulting Markov chain describing this system is of the QBD type. We show that the resulting R matrix associated with this Markov chain has a very special structure which reduces to the solution of a smaller dimension matrix. We then show how to obtain the key performance measures for this system. Of interest is the approach used for obtaining the waiting time distribution. Some numerical examples are also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Survey of incidence of Clostridium difficile infection in Canadian hospitals and diagnostic approaches

A questionnaire relating to Clostridium difficile disease incidence and diagnostic practices was sent to 380 Canadian hospitals (all with > 50 beds). The national questionnaire response rate was 63%. In-house testing was performed in 17.6, 61.5, and 74.2% of the hospitals with < 300, 300 to 500, and > 500 beds, respectively. The average test positivity rates were 17.2, 15.3, and 13.2% for hospitals with < 300, 300 to 500, and > 500 beds, respectively. The average disease incidences were 23.5, 30.8, and 40.3 cases per 100,000 patient days in the hospitals with < 300, 300 to 500, and > 500 beds, respectively. In the 81 hospitals where in-house testing was performed, cytotoxin testing utilizing tissue culture was most common (44.4%), followed by enzyme-linked immunosorbent assay (38.3%), culture for toxigenic C. difficile (32.1%), and latex agglutination (13.6%). The clinical criteria for C. difficile testing were variable, with 85% of hospitals indicating that a test was done automatically if ordered by a doctor. Our results show that C. difficile-associated diarrhea is a major problem in hospitals with > or = 200 beds. Despite a lower disease incidence in smaller hospitals, there was a higher diagnostic test positivity rate. This may reflect the preference of smaller hospitals for culture and latex agglutination tests.     

Lifetime replacement policy in discrete time for a single unit system

We consider, in discrete time, a single unit system which operates for a period of time represented by a general distribution. This unit is subjected to failures during operations. Some of these failures are repairable and the unit is repaired in the repair facility. When the unit experiences a non-repairable failure then it has to be replaced with a new one. We consider a replacement policy based on the lifetime of the unit. This policy can be studied from two different approaches. The first approach, named Model I, is to replace the unit by a new one when the unit attains a predetermined lifetime. The other approach, named Model II, is to close repair facility when the lifetime of the unit attains a predetermined quantity. For each model, we obtain the stationary distribution and some performance measures of interest.     

Computationally efficient method for analyzing guard channel schemes

Call admission control (CAC) is important for cellular wireless networks in order to provide quality of service (QoS) requirements to users. Guard channel scheme is one of the CAC schemes. There are different computational models for analyzing the guard channel scheme which make unrealistic assumption of exponential distribution for both call holding duration and cell residence time for computational tractability. On the other hand, there are some more realistic models for guard channel schemes which capture general distributions of call holding duration and cell residence time by phase type distributions but are computationally cumbersome to implement. The state-spaces of the Markov chains for those models make the computation intractable. In this paper, we develop a tractable computational model to analyze guard channel scheme with general cell residence time and call holding duration captured by phase type distributions. We make our mathematical model computationally tractable by keeping track of the number of calls in different phases of the channel holding time instead of the phase of the channel holding time of individual calls.     

Optimal spectrum utilisation in cognitive radio networks based on processor sharing techniques

Cognitive radio networks have achieved higher efficiency in terms of spectrum usage; however they do not readily solve any competition for access among secondary users. Optimisation is applied to an underlay network to obtain the optimal solution for at least two secondary users operating simultaneously on the same channel. Performance measures are used as the target for optimisation. However, the objective function is difficult to obtain in closed form. For the performance measures, queueing theory, particularly weighted processor sharing techniques are employed to model the system dynamics and behaviour. Transmission power and the interference temperature limit are used to allocate weights to the secondary users. Queue length and waiting time functions obtained from the queuing models are used for optimisation. After establishing that the objective function can be considered to be pseudo‐convex, convex programming is then deployed to obtain the optimised solution. The results suggest that there is indeed an improvement in network performance after optimisation. The immediate benefits of such a system are firstly improved spectrum utilisation through adding multiple secondary users and secondly, through optimisation, higher performance that can be achieved by the secondary users.     

Secure spectrum sensing in relay-based cognitive radio networks

Wireless Networks - A novel cooperative spectrum sensing algorithm intended for robust sensing in the presence of Byzantine attacks was formulated for relay-based cognitive radio networks, with the...