ANALYSIS OF BULK ARRIVALS IN QUEUEING MODELS

       Present paper surveys the literature on bulk queueing models. The concept of bulk arrivals and bulk services has gained a tremendous significance in present situations. Due to congestion problem everywhere (banks, metro stations, bus stops, railway reservation, traffic … etc.) researchers have to focus their attention to develop models and mechanism to deal with the same. A number of models have been developed in the area of queueing theory incorporating bulk queueing models. These bulk queueing models can be applied to resolve the congestion problems. Through this survey, an attempt has been made to review the work done on bulk queues, modeling various phenomenons. The goal is to provide sufficient information to analysts, managers and industry people who are interested in using queueing theory to model congestion problems and want to locate the details of relevant models

Mathematical Models of Multiserver Queuing System for Dynamic Performance Evaluation in Port

We discuss dynamic system performance evaluation in the river port utilizing queuing models with batch arrivals. The general models of the system are developed. This system is modelled by MX/M/n/m queue with finite waiting areas and identical and independent cargo-handling capacities. The models are considered with whole and part batch acceptance (or whole and part batch rejections) and the interarrival and service times are exponentially distributed. Results related to the batch blocking probability and the blocking probability of an arbitrary vessel in nonstationary and stationary states have been obtained. Numerical results and computational experiments are reported to evaluate the efficiency of the models for the real system

Markov denumerable process and queue theory

In this thesis, we study a modified Markovian batch-arrival and bulk- service queue including finite states for dependent control. We first consider the stopped batch-arrival and bulk-service queue process Q∗, which is the process with the restriction of the state-dependent control. After we obtain the expression of the Q∗-resolvent, the extinction probability and the mean extinction time are explored. Then, we apply a decomposition theorem to resume the stopped queue process back to our initial queueing model, that is to find the expression of Q-resolvent. After that, the criteria for the recurrence and ergodicity are also explored, and then, the generating function of equilibrium distribution is obtained. Additionally, the Laplace transform of the mean queue length is presented. The hitting time behaviors including the hitting probability and the hitting time distribution are also established. Furthermore, the busy period distribution is also obtained by the expression of Laplace transform. To conclude the discussion of the queue properties, a special case that m = 3 for our queueing model is discussed. Furthermore, we consider the decay parameter and decay properties of our initial queue process. First of all, similarly we consider the case of the stopped queue process Q∗. Based on this q-matrix, the exact value of the decay parameter λC is obtained theoretically. Then, we apply this result back to our initial queue model and find the decay parameter of our initial queueing model. More specifically, we prove that the decay parameter can be expressed accurately. After that, under the assumption of transient Q, the criteria for λC -recurrence are established. For λC -positive recurrent examples, the generating function of the λC-invariant measure and vector are explored. Finally, a simple example is provided to end this thesis

Markovian bulk-arrival and bulk-service queues with state-dependent control

We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored. opyright © 2011 Elsevier B.V. All rights reserve