Compound Poisson Arrivals Research Articles

Performance evaluation of a distributed energy model with compound Poisson arrivals on an improvised forked network: A detailed analysis

Performance evaluation of a distributed energy model with compound poisson arrivals on an improvised forks network discusses the usage and operations on communication networks, the utilization of these network models had changed the scenario of communication around the world. Establishment and working with these networks lead to work efficiently and effectively for various modes of communications like voice transmission and data transmission. In the current network model, we had considered and developed the network model for the arrival of packets to the network model following non-homogeneous compound poisson arrivals with a uniform distribution pattern. The current model compares with the other homogeneous arrival of packets which follow the Duane process of arrival of packets to the network. When considering energy preservation, it is possible to enhance end-user performance while simultaneously decreasing energy consumption for the mean number of packets, throughput, network node utilization, and dynamic bandwidth utilization. After Implementation of the model, it is observed that energy reservation of the network nodes had increased a lot. During high traffic, our model demonstrates that its emptiness with the comparison of the homogenous model like poisson process and duan process was more efficient with a percentage increase of 16 % and 19 % respectively for a homogeneous network, mean number of packets with a rise of 10 % and 37 %, utilization of packets with 11 % and 18 %, mean delay of packets with 16 % and 5% and throughput of the network with 47 % and 38 %. The results obtained from the equation models were derived and developed with the help of the software MATLAB and MATHCAD. Comparing our heterogeneous model with the results of the homogenous network model had enormously decreased the computational time of the network. Thus, we can clearly state that our proposed model outperformed than remaining other homogenous models.

Compound intervened poisson distribution through one server queuing model with non-homogeneous compound poisson arrivals in bulk and its service rates

Queuing models are used to determine the pragmatic approach in different fields of engineering, sciences, and allied areas. Most of these, the arrivals are dependent on time and would be described by a Poisson process which is non-homogeneous. In this research paper, a one-server queuing model with model with non-homogeneity compound Poisson bulk arrivals has been studied with Compound Intervention Poisson distribution (CIPD). It is observed that the system performance measures are highly influenced by non-homogeneous bulk arrivals rate and batch size distribution parameters. Simulated studies presented that the intervened and compound intervened parameter increases the service rate in terms of utilization, the mean number of customer who undertakes service and emptiness pattern in the queue. Sensitivity analysis has been carried out for the developed model. Non-Homogeneous Poisson process, bulk arrivals, state dependent service rates, Compound Intervened Poisson distribution

Congestion probabilities in OFDM wireless networks with compound Poisson arrivals

The authors study the downlink of an orthogonal frequency division multiplexing (OFDM) based cell that services calls from different service-classes with various resource requirements. They assume that calls arrive in the cell as batches according to a compound Poisson process. They consider that the batch size is generally distributed while each call of a batch is treated separately from the other calls of the same batch, according to the complete sharing policy. To determine the most important performance metrics, i.e. congestion probabilities and resource utilisation in this OFDM-based cell, they model it as a multirate loss model, show that the steady-state probabilities can be determined via a product form solution (PFS) and propose recursive formulas which reduce the complexity of the calculations. In addition, they study the bandwidth reservation (BR) policy which can be used for the reservation of subcarriers in order to favour service-classes whose calls have high subcarrier requirements. The existence of the BR policy destroys the PFS of the steady-state probabilities. However, they show that there exist recursive formulas for the determination of the various performance measures. Simulation verifies the accuracy of the proposed formulas.

MX/G/1 Vacation Queueing System with Two Types of Repair facilities and Server Timeout

We consider a single server vacation queue with two types of repair facilities and server timeout. Here customers are in compound Poisson arrivals with general service time and the lifetime of the server follows an exponential distribution. The server find if the system is empty, then he will wait until the time ‘c’. At this time if no one customer arrives into the system, then the server takes vacation otherwise the server commence the service to the arrived customers exhaustively. If the system had broken down immediately, it is sent for repair. Here server failure can be rectified in two case types of repair facilities, case1, as failure happens during customer being served willstays in service facility with a probability of 1-q to complete the remaining service and in case2 it opts for new service also who joins in the head of the queue with probability q. Obtained an expression for the expected system length for different batch size distribution and also numerical results are shown.

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.

Queueing Systems of INAR(1) Processes with Compound Poisson Arrivals

Integer valued autoregressive processes of order 1 (or INAR(1) processes) that may be interpreted as discrete time G/Geom/∞ queue length processes are considered. The arrivals are assumed to be compound Poisson distributed. It is shown that then the stationary distribution of the queue length process as well as the distribution of the departures from the system are again members of the class of compound Poisson distributions. This reveals remarkable invariance properties of the model. The derived explicit expressions allow for the calculation of important performance measures. It is further shown that time-reversibility of the queue length process as well as an analogue of Burke’s theorem hold only if the arrival process is Poisson.

The processor-sharing queue with bulk arrivals and phase-type services

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue...

The processor-sharing queue with bulk arrivals and phase-type services

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.

Analysis of a Batch Arrival Poisson Queue Under Single Vacation Policy

We consider a single server Markovian queueing system with compound Poisson arrivals of batches of random size under a single vacation policy, where the server takes exactly one vacation between two successive busy periods. We are concerned with the steady state distributions of the additional queue size, additional delay and queue waiting time distribution.

The MM CPP/GE/c G-Queue: Sojourn Time Distribution

We obtain the sojourn time probability distribution function at equilibrium for a Markov modulated, multi-server, single queue with generalised exponential (GE) service time distribution and compound Poisson arrivals of both positive and negative customers. Such arrival processes can model both burstiness and correlated traffic and are well suited to models of ATM and other telecommunication networks. Negative customers remove (ordinary) customers in the queue and are similarly correlated and bursty. We consider both the cases where negative customers remove positive customers from the front and the end of the queue and, in the latter case, where a customer currently being served can and cannot be killed by a negative customer. These cases can model an unreliable server or load balancing respectively. The results are obtained as Laplace transforms and can be inverted numerically. The MM CPP/GE/c G-Queue therefore holds the promise of being a viable building block for the analysis of queues and queueing networks with bursty, correlated traffic, incorporating load balancing and node-failures, since the equilibrium behaviour of both queue lengths and response times can be determined in a tractable way.

WAITING TIMES AT PERIODICALLY SWITCHED ONE-WAY TRAFFIC LANES

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules (i.e., the driving direction on the infrastructure is switched between two directions according to a fixed time schedule). We analyze both symmetric and asymmetric systems (i.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random setup times and periodic (nonexhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1–2% for Poisson arrivals. Also, we indicate how our approximations can be generalized to compound Poisson arrivals.

Optimal control of batch service queues with finite service capacity and linear holding costs

We consider the optimal control problem of certain batch service queueing systems with compound Poisson arrivals and linear holding costs. The control problem involves the determination of the epochs at which the service is initiated as well as the sizes of the batches served. The service times are assumed to be independent and identically distributed, however, with a general distribution. A quite natural operating policy is to start the service as soon as the number of customers reaches some threshold and serve always as many customers as possible. Assuming infinite service capacity Deb [4] proved that under some mild conditions the optimal operating policy is of this type. In this paper we show that a similar result is valid even if the service capacity is finite. In this case the threshold is never greater than Q, the service capacity (the maximum number of customers that can be served at the same time).

Optimal control of batch service queues with compound Poisson arrivals and finite service capacity

We consider the optimal control problem of an M X /G(Q)/1 batch service queueing system with Q<∞. So, we assume that customers arrive according to a compound Poisson process and are served in batches not greater than the finite service capacity Q. The control problem involves the determination of the epochs at which the service is initiated as well as the sizes of the batches served. We introduce a new class of operating policies and prove that, under some additional assumptions, there is an optimal operating policy belonging to this new class.

Optimal dispatching of an infinite capacity shuttle with compound poisson arrivals: Control at a single terminal

We consider the optimal control of an infinite capacity shuttle which transports passengers between two terminals. Passengers arrive at each of two terminals according to independent compound Poisson processes. The travel time from one terminal to the other one is a random variable following an arbitrary distribution. The dispatcher can hold the shuttle at only one of the terminals. Thus, when the shuttle is dispatched at terminal 1, it transports all the passengers waiting at terminal 1 to terminal 2 and instantaneously picks up the passengers at terminal 2 and returns to terminal 1. Assuming that the dispatcher has complete information about the number of passengers waiting at each terminal, we consider the following control limit policy: dispatch the shuttle if, and only if, the total number of passengers waiting at both terminals is at least as large as some prespecified control limit, m. In this paper, under a linear cost structure, we provide an explicit expression for the expected cost per unit time as a function of the control value, m, and present a simple and efficient method for computing the optimal control value.

On pseudo-conservation laws for the cyclic server system with compound Poisson arrivals

Boxma and Groenendijk obtain the pseudo-conservation laws for cyclic server systems, for both the continuous-time system with simple Poisson arrivals, and for the discrete-time system. We extend these laws to the continuous-time cyclic server system with compound Poisson arrivals. In the process we identify an error in Boxma and Groenendijk's analysis of the semi-exhaustive service strategy in the discrete-time cyclic server system.

Optimality of threshold policies in single-server queueing systems with server vacations

In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. We show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the system empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

Optimality of threshold policies in single-server queueing systems with server vacations

In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. We show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the system empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

The shuttle dispatch problem with compound Poisson arrivals: Controls at two terminals

We consider the control of an infinite capacity shuttle which transports passengers between two terminals. The passengers arrive at each terminal according to a compound Poisson process and the travel time from one terminal to the other is a random variable following an arbitrary distribution. The following control limit policy is considered: dispatch the shuttle at terminali, at the instant that the total number of passengers waiting at terminali reaches or exceeds a predetermined control limitm i . The objective of this paper is to obtain the mean waiting time of an arbitrary passenger at each terminal for given control valuesm 1 andm 2. We also discuss a search procedure to obtain the optimal control values which minimize the total expected cost per unit time under a linear cost structure.

A Functional Equation Arising in a Queue With a Gating Mechanism

Our primary aim in this paper is to study a functional equation that arises in a problem of queueing. Consider a queue with compound Poisson arrivals and general service times with a gating mechanism. The gating mechanism takes in at most m(≤∞) customers at a time for service and serves these customers according to the processor-sharing discipline. In this paper, we examine various performance characteristics for this queue. The characteristics include waiting-time distribution, queue-length distribution, time spent with the server, and batch-size distribution for service.

Response times in gated M/G/1 queues: The processor-sharing case

A class of single server queues with Poisson arrivals and a gated server is considered. Whenever the server becomes idle the gate separating it from the waiting line opens, admitting all the waiting customers into service, and then closes again. The batch admitted into service may be served according to some arbitrary scheme. The equilibrium waiting time distribution is provided for the subclass of conservative schemes with arbitrary service times and the processor-sharing case is treated in some detail to produce the equilibrium time-in-service and response time distributions, conditional on the length of required service. The LIFO and random order of service schemes and the case of compound Poisson arrivals are treated briefly as examples of the effectiveness of the proposed method of analysis. All distributions are provided in terms of their Laplace transforms except for the case of exponential service times where the L.T. of the waiting time distribution is inverted. The first two moments of the equilibrium waiting and response times are provided for most treated cases and in the exponential service times case the batch size distribution is also presented.