Finite-buffer Queue Research Articles

Analysis of multiple sleeps and N-policy on a M/G/1/K user request queue in 5g networks base station

The primary purpose of green communication is to reduce energy use. The base station (BS) is a radio receiver/transmitter that acts as the wireless network’s hub. It serves as a link between a wired and wireless network. To receive and transmit messages, BS uses a lot of energy. The use of effective sleep and wake-up/setup activities with an acceptable delay helps reduce base station power consumption. In this paper, the BS’s service process is modelled as a finite buffer queue with close down, sleep, and setup. After a certain number of user requests (URs) have accumulated in the system, to awaken the BS from multiple sleeps (MS) the -Policy is implemented. To produce probability generating functions, the supplementary variable approach is applied. The UR’s mean delay and the BS’s mean power consumption are calculated using simulation. According to computational studies, multiple sleeps with -policy consume less power than multiple sleeps without -policy.

Analysis of single server finite buffer queue under discouraged arrival and retention of reneging

Queuing models where arrival rates go down consequent to increase in the number of customers are called systems with discouraged arrivals. Discouraged arrivals are distinct from balking in the sense that balking implies that arriving customers do not join. In this paper, we model a single server finite buffer Markovian queuing model with discouraged arrival, balking, reneging and retention of reneged customers. The steady state probabilities are obtained using Markov process method. Closed form expression of traditional as well as some freshly designed performance measures are presented. We also perform sensitivity analysis to examine the variations in performance measures with the variations in system parameters. Our results are numerically illustrated through a field level problem with design connotations.

Burst ratio for a versatile traffic model.

We deal with a finite-buffer queue, in which arriving jobs are subject to loss due to buffer overflows. The burst ratio parameter, which reflects the tendency of losses to form long series, is studied in detail. Perhaps the most versatile model of the arrival stream is used, i.e. the batch Markovian arrival process (BMAP). Among other things, it enables modeling the interarrival time density function, the interarrival time autocorrelation function and batch arrivals. The main contribution in an exact formula for the burst ratio in a queue with BMAP arrivals and arbitrary service time distribution. The formula is presented in an explicite, ready-to-use form. Additionally, the impact of various system parameters on the burst ratio is demonstrated in numerical examples. The primary application area of the results is computer networking, where the complex nature of traffic has a deep impact on the burst ratio. However, due to the versatile arrival model, the results can be applied in other fields as well.

Per-flow structure of losses in a finite-buffer queue

We analyze the structure of losses in individual flows, in a multi-flow, finite-buffer queueing system. Namely, a model with many separate flows (streams) of jobs arriving to a shared buffer, where they are subject to losses due to buffer overflows, is considered. (Such systems are common, for instance, in computer networking, where flows of packets arrive to the same router’s buffer from different network users). Assuming a general service time distribution and Poisson flows, we study the burst ratio parameter, which reflects the tendency of losses to cluster together, in long series. In particular, an explicit formula for the burst ratio in each individual flow is derived. Using this formula we show, among other things, that the per-flow burst ratio may vary significantly among flows and differ from the global burst ratio. This distinguishes the per-flow burst ratio from the per-flow loss ratio, which is the same for all flows. We demonstrate also the dependence of the per-flow burst ratio on the flow rate, number of flows, buffer size, system load and variance of the service time.

N , n -Preemptive-Priority M/G/1 Queues with Finite and Infinite Buffers

In this paper, we analyze an M/G/1 priority queueing model with finite and infinite buffers under the N , n -preemptive priority discipline, under which preemption decisions are made based on the number of high-priority customers. This priority queueing model can be used for the performance analysis of communication systems accommodating delay- and loss-sensitive packets simultaneously. To analyze the proposed model, we extend the method of delay cycle analysis and develop a queue length version of it for finite-buffer queues. Throughout our analysis, we demonstrate that by the proposed method the analysis of the complex priority queueing model can be reduced to that of simple delay cycles, so two different preemption modes of the queueing model can be dealt with in a unified way. The numerical study reveals that adjusting the decision variables N and n allows us to fine-tune system performance for different classes of customers, and N operates as a primary control variable, regardless of the preemption mode and service-time distributions.

Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy.

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

Probabilistic Analysis of a Buffer Overflow Duration in Data Transmission in Wireless Sensor Networks

One of the most important problems of data transmission in packet networks, in particular in wireless sensor networks, are periodic overflows of buffers accumulating packets directed to a given node. In the case of a buffer overflow, all new incoming packets are lost until the overflow condition terminates. From the point of view of network optimization, it is very important to know the probabilistic nature of this phenomenon, including the probability distribution of the duration of the buffer overflow period. In this article, a mathematical model of the node of a wireless sensor network with discrete time parameter is proposed. The model is governed by a finite-buffer discrete-time queueing system with geometrically distributed interarrival times and general distribution of processing times. A system of equations for the tail cumulative distribution function of the first buffer overflow period duration conditioned by the initial state of the accumulating buffer is derived. The solution of the corresponding system written for probability generating functions is found using the analytical approach based on the idea of embedded Markov chain and linear algebra. Corresponding result for next buffer overflow periods is obtained as well. Numerical study illustrating theoretical results is attached.

On transient queue-size distribution in a finite-buffer model with threshold waking and early setup policy

A finite-buffer queueing system with threshold waking and early setup policy is investigated. The arrival stream is governed by a Poisson process while service times are assumed to be generally distributed. The natural FIFO processing discipline is used. Every time when the system empties, a type-specific energy saving policy is initialized that is a mixture of the classical N-type policy and an early setup mechanism. Namely, if the level of accumulated messages reaches M≤N, a generally distributed setup time is started, during which the service station achieves full readiness for processing. If, at the completion epoch of the setup time, the state of the system (the number of accumulated messages) equals at least N, then the service begins immediately. Otherwise, the service station waits (being ready for processing) for the Nth arrival. The representation for the Laplace transform of the transient queue-size distribution is obtained using the analytical approach based on the idea of embedded Markov chain, the formula of total probability, linear algebra and renewal theory. A numerical example and simulational study are attached.

The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time

In this paper, we study the discrete-time MAP/PH/1 queue with multiple working vacations and finite bufferN. Using the Matrix-Geometric Combination method, we obtain the stationary probability vectors of this model, which can be expressed as a linear combination of two matrix-geometric vectors. Furthermore, we obtain some performance measures including the loss probability and give the limit of loss probability as finite bufferNgoes to infinite. Waiting time distribution is derived by using the absorbing Markov chain. Moreover, we obtain the number of customers served in the busy period. At last, some numerical examples are presented to verify the results we obtained and show the impact of parameterNon performance measures.

Queue and Loss Distributions in Finite-Buffer Queues

We derive simple bounds on the queue distribution in finite-buffer queues with Markovian arrivals. The bounds capture a truncated exponential behavior, involving joint horizontal and vertical shifts of an exponential function; this is fundamentally different than existing results capturing horizontal shifts only.We also obtain similar bounds on the loss distribution, which is a key metric to understand the impact of finite-buffer queues on real-time applications. Simulations show that the bounds are accurate in heavy-traffic regimes, and improve existing ones by orders of magnitude.

Queue and Loss Distributions in Finite-Buffer Queues

We derive simple bounds on the queue distribution in finite-buffer queues with Markovian arrivals. Our technique relies on a subtle equivalence between tail events and stopping times orderings. The bounds capture a truncated exponential behavior, involving joint horizontal and vertical shifts of an exponential function; this is fundamentally different than existing results capturing horizontal shifts only. Using the same technique, we obtain similar bounds on the loss distribution, which is a key metric to understand the impact of finite-buffer queues on real-time applications. Simulations show that the bounds are accurate in heavy-traffic regimes, and improve existing ones by orders of magnitude. In the limiting regime with utilization ρ=1 and iid arrivals, the bounds on the queue size distribution are insensitive to the arrivals distribution.

Analyzing of a finite buffer queue with finite number of vacation policy and correlated arrivals

This paper analyses a MAP/G/1/N queue having finite number of vacations. The server takes a finite number (say J ≥ 0) of vacations whenever the system becomes empty at service completion epoch. If no clients are found by the end of the Jth vacation, the server does not go for vacation and stays in the system (called dormant period) until one client arrives. The number of vacations being finite and the server can utilise vacation periods for any other jobs. This is obvious that J = 1 and J → 1 lead to single and multiple vacation models, respectively. This research work mainly focuses more generalised vacation policy and different use cases. The following results have been obtained: 1) the distributions of clients in the queue at various epochs; 2) the Laplace-Stieltjes transform of the actual waiting-time distribution in the queue of a client under the FCFS discipline. The numerical data and graphs are presented to establish the analytical result.

Analysing a finite buffer queue with finite number of vacation policy and correlated arrivals

Analysing a finite buffer queue with finite number of vacation policy and correlated arrivals

A cross layer framework of Radio Resource Allocation for QoS provisioning in multi-channel fading wireless networks

In this paper, we present an analytical framework for the performance evaluation of Radio Resource Allocation (RRA) in Orthogonal Frequency Division Multiple Access (OFDMA) networks. We focus on Quality of Service (QoS) guaranteed traffic whose capacity, in terms of the number of active user connections, depends on the users’ QoS requirements and channel conditions, and the RRA algorithm. The required QoS is guaranteed by restricting the number of admitted calls, which in turn requires an accurate estimate of the QoS metrics and capacity supported by the RRA when a new call arrives. These estimates for OFDMA networks are variable and usually obtained through time-consuming offline computer simulations. Mathematical frameworks on the other hand yield timely and accurate results. However, earlier known works on analytical modelling of RRA either consider a single channel with random traffic arrivals or multiple channels with full buffer data traffic. In contrast, we develop a queueing theoretic framework considering randomly arriving QoS-guaranteed traffic in a variable-rate multi-channel multi-class OFDMA network. The framework can be used online leading to better dynamic Call Admission Control. We characterize the RRA algorithm using a scheduler control parameter which can regulate the call blocking probability while providing predefined QoS constraints. We model the RRA as a variable service rate, multi-server, multi-class, finite buffer queueing system and verify the derived QoS metrics using extensive Monte-Carlo discrete event simulations.

Burst ratio in the finite-buffer queue with batch Poisson arrivals

We study the burst ratio in the queueing system with finite buffer and batch arrivals. The study is motivated by computer networking, in which packet losses occur due to queueing mechanisms and buffer overflows. First, we derive the formula for the burst ratio in the case of compound Poisson arrivals, general distribution of the service time and general distribution of the batch size. Then, we study its asymptotic behavior, as the buffer size grows to infinity. Using the obtained analytical solutions, we present several numerical examples with various batch size distributions, service time distributions, buffer sizes and system loads. Finally, we compare the computed burst ratios with values obtained in simulations.

Transient solution for the queue-size distribution in a finite-buffer model with general independent input stream and single working vacation policy

• Transient queue-size distribution in GI/M/1/N-type model with working vacation policy is studied. • The idea of embedded Markov chain, total probability law and linear algebra are applied. • Final result is given for the Laplace transform in a compact form. • Illustrative numerical examples are attached. A single-channel finite-buffer queueing model with a general independent input stream of customers, exponential processing times and a working vacation policy is considered. Every time , when the server becomes idle, an exponentially distributed single working vacation period is being initialized, during which the processing is provided with another (slower) rate. After the completion of the vacation period, the service is being continued normally, with the original speed. Using the idea of an embedded Markov chain, the systems of Volterra-type integral equations for the time-dependent queue-size distributions, conditioned by the initial buffer state and related to each other, are built for models beginning the operation in normal and working vacation modes, separately. The solutions of the corresponding systems written for the Laplace transforms are obtained in compact forms using the linear algebraic approach. The numerical illustrative examples are attached as well.

On the Queue Length Distribution in BMAP Systems

Batch Markovian Arrival Process – BMAP – is a teletraffic model which combines high ability to imitate complexstatistical behaviour of network traces with relative simplicity in analysis and simulation. It is also a generalization of a wide class of Markovian processes, a class which in particular include the Poisson process, the compound Poisson process, the Markovmodulated Poisson process, the phase-type renewal process and others. In this paper we study the main queueing performance characteristic of a finite-buffer queue fed by the BMAP, namely the queue length distribution. In particular, we show a formula for the Laplace transform of the queue length distribution. The main benefit of this formula is that it may be used to obtain both transient and stationary characteristics. To demonstrate this, several numerical results are presented.

Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented.

An algorithmic analysis of the [formula omitted] generalized processor-sharing queue

This paper deals with the analysis of the BMAP/MSP/1 generalized processor-sharing queue. The analysis is based on RG-factorization technique applied to the Markov chain of the associated quasi-birth and death process. The stationary system-length distribution of the number of customers in the system and the Laplace–Stieltjes transform (LST) of the sojourn time distribution of a tagged customer in the system is obtained in this paper. The mean sojourn time of a tagged customer is derived using the previous LST. The corresponding finite-buffer queueing model is also analyzed and system-length distribution is derived using the same technique as stated above. Further, the blocking probabilities for customers with different positions, such as the first-, an arbitrary- and the last-customer of a batch are obtained. The detail computational procedure for these models is discussed. Various numerical results are presented to show the applicability of the results obtained in the study.