Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. Th...

One of the classical models of queueing theory is the M/M/s queue or Erlang delay model. This model has s homogeneous servers working in parallel. Customers arrive according to a Poisson process with arrival rate λ, and the service times are independent and exponentially distributed with mean 1/μ. Let the offered load be a = λ/μ and assume a < s to have a proper steady-state distribution. The m...

Abstract Nature is never at a steady state. Natural history generated by ever-new and ever-interacting forces that produce continuous changes. At virtually all timescales, the geological record shows these changes do not cancel each other out and, thus, state utopic. However, we need of equilibrium as starting point for modelling Nature, steady-state condition widely used reference in idealisat...

We consider a single server queueing system with two types of traffic where traffic of type 1 (such as data) are delay-insensitive and loss-sensitive and traffic of type 2 (such as voice) are delay-sensitive and loss-insensitive. To provide the required Quality of Service (QoS) of each type of traffic, we adopt the strict priority scheme for delay and push-out scheme with threshold for loss. Th...

Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...

This paper deals with the dependability evaluation of software programs of iterative nature. In this work we define a new model that is able to account for both dependencies between input values of successive iterations and the effects of sequences of consecutive failures. Differently from previously proposed models, it is based on steady state probabilities of an iteration outcome (success, be...

For a birth-death process subject to catastrophes, defined on the state-space S = {r, r+1, r+2,. . .}, with r a positive integer or zero, the first-visit time to a state k ∈ S is considered and the Laplace transform of its probability density function is determined, use of which is then made to obtain mean and variance. The Laplace transform of the probability density function of the first effe...

In this paper, we consider a queueing model for machine repairing system with Bernoulli vacation schedule. The failure times, repair times and vacation times are all assumed to be exponentially distributed. In congestion, the server may increase the repair rate with pressure coefficient  to reduce the queue length. We assume that the server begins the working vacation when the system is empty....

This paper deals with the dependability evaluation of software programs of iterative nature. In this work we define a new model that is able to account for both dependencies between input values of successive iterations and the effects of sequences of consecutive failures. Differently from previously proposed models, it is based on steady state probabilities of an iteration outcome (success, be...

We study the steady-state queue-length vector in a multi-class queue with relative priorities. Upon service completion, the probability that the next served customer is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. We establish a state-space collapse for the scaled queue length vector in the heavy-...