Andrzej Chydziński
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Departure Process of Actively Managed Queue with Dependent Job Sizes Open
We focus on a queueing model in which the sizes of arriving jobs are stochastically dependent and each job may be denied service with a probability determined by the queue size (active management). Both of these effects are known to occur …
Waiting Time in an MSP Queue with Active Management Open
We study waiting times in a queue with active management and correlated job/packet sizes, which induce correlated service times. In the transient case, formulae for the distribution tail, the probability density, and the expected virtual w…
Buffer with Dropping Function and Correlated Packet Lengths Open
We analyze a model of the packet buffer in which a new packet can be discarded with a probability connected to the buffer occupancy through an arbitrary dropping function. Crucially, it is assumed that packet lengths can be correlated in a…
Loss Clustering at MSP Buffer Open
Packet losses cause a decline in the performance of packet networks, and this decline is related not only to the percentage of losses but also to the clustering of them together in series. We study how the correlation of packet sizes influ…
Throughput of Buffer with Dependent Service Times Open
We study the throughput and losses of a buffer with stochastically dependent service times. Such dependence occurs not only in packet buffers within TCP/IP networks but also in many other queuing systems. We conduct a comprehensive, time-d…
Workload of Queueing Systems with Autocorrelated Service Times Open
The queuing model with autocorrelated service times is studied with respect to workload, i.e., the time needed to serve all the customers in the queue. Specifically, new formulas for the probability density of workload, its tail, the avera…
Asymmetry Between Queues with Correlated Service and Correlated Arrivals Open
It is known that a correlation in either the service or interarrival times causes a deterioration in the performance of a queuing system. This study aimed to determine which of the two correlations—in the service times or in the interarriv…
Transient GI/MSP/1/N Queue Open
A non-zero correlation between service times can be encountered in many real queueing systems. An attractive model for correlated service times is the Markovian service process, because it offers powerful fitting capabilities combined with…
Buffer with N Policy and Active Management Open
The N policy is a buffer and transmission management scheme proposed for nodes in wireless sensor networks to save energy. It exploits the concept that the output radio of a node is initially switched off until a critical queue of packets …
Level-Crossing Characteristics of an Actively Managed Buffer Open
In this paper, we examine a buffer with active management that rejects packets basing on the buffer occupancy. Specifically, we derive several metrics characterizing how effectively the algorithm can prevent the queue of packets from becom…
Response Time of Queueing Mechanisms Open
We study response time, a key performance characteristic of queueing mechanisms. The studied model incorporates both active and passive queue management, arbitrary service time distribution, as well as a complex model of arrivals. Therefor…
Output Stream from the AQM Queue with BMAP Arrivals Open
We analyse the output stream from a packet buffer governed by the policy that incoming packets are dropped with a probability related to the buffer occupancy. The results include formulas for the number of packets departing the buffer in a…
Loss Process at an AQM Buffer Open
We perform a comprehensive analysis of packet losses occurring at an AQM buffer in which the packet deletion probability is relative to the size of the queue. Several characteristics of the loss process are derived: the number of deletions…
On the Influence of AQM on Serialization of Packet Losses Open
We study the influence of the active queue management mechanism based on the queue size on the serialization of packet losses, i.e., the occurrences of losses in long, consecutive series. We use a traffic model able to mimic precisely the …
Non-Stationary Characteristics of AQM Based on the Queue Length Open
We performed a non-stationary analysis of a class of buffer management schemes for TCP/IP networks, in which the arriving packets were rejected randomly, with probability depending on the queue length. In particular, we derived formulas fo…
Waiting Time in a General Active Queue Management Scheme Open
We derive the waiting time in a queueing scheme, in which an arriving job can be denied service with probability relative to the queue size. Such scheme is a generalization of the tail-drop queue, in which the job is denied service when th…
Burst Ratio of Packet Losses in Individual Network Flows Open
We study the burst ratio of packet loss processes in networking. This parameter characterizes the inclination of packet losses to form long, consecutive sequences. Such long sequences of losses may have a negative impact on multimedia stre…
Throughput of the Queue With Probabilistic Rejections Open
The queueing system with probabilistic job rejections based on the system occupancy has applications in engineering and logistics. It is also a natural extension of the most basic and commonly used FIFO queue with tail drop. In this paper,…
Impact of the Dropping Function on Clustering of Packet Losses Open
The dropping function mechanism is known to improve the performance of TCP/IP networks by reducing queueing delays and desynchronizing flows. In this paper, we study yet another positive effect caused by this mechanism, i.e., the reduction…
Burst ratio for a versatile traffic model Open
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 …
Per-flow structure of losses in a finite-buffer queue Open
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 …
AQM based on the queue length: A real-network study Open
Active Queue Management (AQM) is recommended by Internet Engineering Task Force to mitigate the bufferbloat phenomenon in the Internet. In this paper, we show the results of comprehensive measurements carried out in our university network,…
On the stability of queues with the dropping function Open
In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the wor…
On the structure of data losses induced by an overflowed buffer Open
We deal with the statistical structure of data losses, when packetized data are transmitted through a channel with a buffering mechanism and may be subject to losses due to the buffer overflow. The main contribution is an explicit formula …
On the stability of queues with the dropping function Open
In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the wor…
On the Transient Queue with the Dropping Function Open
We deal with a queueing system, in which arriving packets are being dropped with the probability depending on the queue size. Such a scheme is used in several active queue management schemes proposed for Internet routers. In this paper, we…
Response time of the queue with the dropping function Open
In many active queue management algorithms, the dropping function, which associates the probability of dropping a packet with the buffer occupancy, is used. Several different forms of the dropping function has been considered so far, from …
Queues With the Dropping Function and Non-Poisson Arrivals Open
We deal with the single-server queueing system, in which an arriving job (packet, customer) is not allowed to the queue with the probability depending on the queue size. Such a rejected job is lost and never returns to the queue. The study…
Queues with the dropping function and general service time Open
We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas …