Stability analysis for retrial queue with collisions and r-persistent customers

We consider a single server retrial queue with general distribution of service times, collisions and r-persistent customers. The last phenomena describes the behaviour of customers that are leaving the system immediately if the server is busy upon arrival. We consider the system with customers, which leave the system without servicing with constant probability r. We provide the numerical stability analysis in such system using the following approach. First, we build the diffusion limit for the number of customers in the orbit and then analyze its drift coefficient. For different system parameters, we have different stability conditions

Diffusion approximation for retrial queue with collisions and non-persistent customers

This paper is devoted to the analysis of retrial queue with an arbitrary distribution of service times, collisions, and non-persistent customers. Our aim is to investigate the number of customers in the orbit of the system. To this end, we use the asymptotic-diffusion method to build a diffusion approximation for the steady-state distribution of the number of customers in the orbit

Diffusion limit for single-server retrial queues with renewal input and outgoing calls

This paper studies a single-server retrial queue with two types of calls (incoming and outgoing calls). Incoming calls arrive at the server according to a renewal process, and outgoing calls of N − 1 (N ≥ 2) categories occur according to N − 1 independent Poisson processes. Upon arrival, if the server is occupied, an incoming call joins a virtual infinite queue called the orbit, and after an exponentially distributed time in orbit enters the server again, while outgoing calls are lost if the server is busy at the time of their arrivals. Although M/G/1 retrial queues and their variants are extensively studied in the literature, the GI/M/1 retrial queues are less studied due to their complexity. This paper aims to obtain a diffusion limit for the number of calls in orbit when the retrial rate is extremely low. Based on the diffusion limit, we built an approximation to the distribution of the number of calls in orbit

Mathematical model of Scheduler with Semi-Markov input and bandwidth sharing discipline

In this paper, we consider single server queueing system with multiple semi-Markov inputs and buffers. Each request of the flows brings to the system some random amount of information. According to the bandwidth sharing discipline, each buffer has its own part of the throughput and the server transmits the information from buffers simultaneously. The aim of the current research is to derive the probability distribution of the amount of information in single buffer

Semi-Markov resource flow as a bit-level model of traffic

In this paper, we consider semi-Markov flow as a bit-level model of traffic. Each request of the flow brings some arbitrary distributed amount of information to the system. The current paper aims to investigate the amount of information received in semi-Markov flow during time unit. We use the asymptotic analysis method under the limit condition of growing time of observation to derive the limiting probability distribution of the amount of information received in the flow and build the approximation of its prelimit distribution function

RQ-система с ненадёжным прибором и разнотипными вызываемыми заявками

Retrial queue under consideration is the model of call center operator switchingbetween input and outgoing calls. Incoming calls form a Poisson point process. Uponarrival, an incoming call occupies the server for an exponentially distributed servicetime if the server is idle. If the server if busy, an incoming call joins the orbit tomake a delay before the next attempt to take the server. The probability distributionof the length of delay is an exponential distribution. Otherwise, the server makesoutgoing calls in its idle time. There are multiple types of outgoing calls in the system.Outgoing call rates are different for each type of outgoing call. Durations of differenttypes of outgoing calls follow distinct exponential distributions. Unsteadiness is thatthe server crashes after an exponentially distributed time and needs recovery. Therates of breakdowns and restorations are different and depend on server state. Ourcontribution is to obtain the probability distribution of the number of calls in theorbit under high rate of making outgoing calls limit condition. Based on the obtainedasymptotics, we have built the approximations of the probability distribution of thenumber of calls in the orbit

Asymptotic analysis of Markovian retrial queue with unreliable server and multiple types of outgoing calls

In this paper, we consider markovian retrial queue with two-way communication and unreliable server. Input process is Poisson with constant rate. Incoming calls that find the server busy join the orbit and reattempt to get the service after an exponentially distributed delay. In its idle time the server makes outgoing calls. There are multiple types of outgoing calls in the system. Service durations and rates of making outgoing calls are different and depend on type of outgoing call. The unsteadyness of the server is characterised by breakdown and restoration periods and its durations are exponentially distributed with rates depending on the server state

Asymptotic-diffusion analysis of multiserver retrial queue with two-way communication

In this paper, we consider multiserver retrial queue with two-way communication. Incomimg calls arrive according to the Poisson process and reserve the server for an exponentially distributed time. If all of the servers are busy the incoming call joins the orbit and makes a delay for an exponentially distributed time before the next attempt to occupy the server. Idle servers also make outgoing calls following a distinct exponential distribution. Using the asymptotic-diffusion analysis method we derive the approximation for the stationary probability distribution of the number of calls in the orbit

Asymptotic-diffusion analysis of retrial queue with two-way communication and renewal input

In this paper, we consider a single server retrial queue with two types of calls. Incoming calls form a renewal input ow. If the server is busy upon arrival the incoming call joins the orbit. After a random delay calls from the orbit make the next attempt to take the server. In its idle time the server makes outgoing calls. We consider the retrial queue with multiple types of outgoing calls. The aim of this paper is to obtain the diusion approximation of the number of calls in the orbit