A relationship between different costs of container yard modelling in port using queuing approach

U ovom radu razmatrani su grupni dolasci kontenera na kontenerskom skladištu koji su modelirani višekanalnim sistemom teorije redova čekanja MX/M/c sa c skladišnih dizalica kao kanalima opsluživanja. Pretpostavljeno je da je veličina grupe kontenera, X (broj kontenera y grupi koja dolazi na kontenersko skladište) distribuirana u skladu sa Puasonovskim tipom raspodele. Koristeći opšti izraz za razmatrani model redova čekanja, izveden je izraz za odnos specifičnih troškova koji sadrži verovatnoće stanja sistema, faktor iskorišćenja sistema, srednju vrednost i disperziju veličine grupe. Primenjujući taj izraz, predstavljeni su odgovarajući numerički i grafički rezultati za 1, 2 i 3 skladišne dizalice na kontenerskom skladištu u luci. Takođe ističemo da dobijeni analitički izraz omogućava diskusiju i poređenje vrednosti odnosa specifičnih troškova razmatranih modela redova čekanja MX/M/c sa različitim parametrima performanse luke, kao i poređenja istih sa odnosom specifičnih troškova u odnosu na redove čekanja istraživanih u prethodnim radovima autora koji se odnose na ovaj problem.In this paper we consider batch arrivals of containers at a port container yard which is modeled as a multi-server queue MX/M/c with c yard cranes for the service. It is assumed that the related group size (the number of containers in an arriving group), X is distributed by a Poisson-like distribution. Using a more general formula for such queue models, here it is deduced the expression for the specific cost ratio involving the state probabilities, the utilization factor, the mean and the variance of the group size. Applying this expression, related numerical and graphical results are presented when the number of yard cranes at container yard in port is 1, 2 or 3. We also point out that this expression allows us to discuss and compare the values of specific cost ratio concerning the considered MX/M/c queues with different port performance parameters, as well as with specific cost ratio of the queues investigated in earlier authors' papers on this topic

A relationship between different costs of container yard modelling in port using queuing approach

U ovom radu razmatrani su grupni dolasci kontenera na kontenerskom skladištu koji su modelirani višekanalnim sistemom teorije redova čekanja MX/M/c sa c skladišnih dizalica kao kanalima opsluživanja. Pretpostavljeno je da je veličina grupe kontenera, X (broj kontenera y grupi koja dolazi na kontenersko skladište) distribuirana u skladu sa Puasonovskim tipom raspodele. Koristeći opšti izraz za razmatrani model redova čekanja, izveden je izraz za odnos specifičnih troškova koji sadrži verovatnoće stanja sistema, faktor iskorišćenja sistema, srednju vrednost i disperziju veličine grupe. Primenjujući taj izraz, predstavljeni su odgovarajući numerički i grafički rezultati za 1, 2 i 3 skladišne dizalice na kontenerskom skladištu u luci. Takođe ističemo da dobijeni analitički izraz omogućava diskusiju i poređenje vrednosti odnosa specifičnih troškova razmatranih modela redova čekanja MX/M/c sa različitim parametrima performanse luke, kao i poređenja istih sa odnosom specifičnih troškova u odnosu na redove čekanja istraživanih u prethodnim radovima autora koji se odnose na ovaj problem.In this paper we consider batch arrivals of containers at a port container yard which is modeled as a multi-server queue MX/M/c with c yard cranes for the service. It is assumed that the related group size (the number of containers in an arriving group), X is distributed by a Poisson-like distribution. Using a more general formula for such queue models, here it is deduced the expression for the specific cost ratio involving the state probabilities, the utilization factor, the mean and the variance of the group size. Applying this expression, related numerical and graphical results are presented when the number of yard cranes at container yard in port is 1, 2 or 3. We also point out that this expression allows us to discuss and compare the values of specific cost ratio concerning the considered MX/M/c queues with different port performance parameters, as well as with specific cost ratio of the queues investigated in earlier authors' papers on this topic

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

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer

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 M-X/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

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 M-X/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

(R1984) Analysis of M^[X1], M^[X2]/G1, G_2^(a,b)/1 Queue with Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback

In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to a , else the server should not start service until a customers have accumulated. Meanwhile priority queue is empty; the server becomes idle or go for vacation. If server gets breakdown while the priority customers are being served, they may wait in the head of the queue and get fresh service after repair completion, but in case of ordinary customers they may leave the system. After completion of each priority service, customer may rejoin the system as a feedback customer for receiving regular service because of inappropriate quality of service. Supplementary variable technique and probability generating function are generally used to solve the Laplace transforms of time-dependent probabilities of system states. Finally, some performance measures are evaluated and express the numerical results

The Mx/G/1 Queue with Unreliable Server, Delayed Repairs, and Bernoulli Vacation Schedule under T-Policy

In this paper we study a batch arrival queuing system. The server may break down while delivering service. However, repair is not provided immediately, rather it is delayed for a random amount of time. At the end of service, the server may process the next customer if any are available, or may take a vacation to execute some other job. Finally, the server implements the T-policy. We describe for this system an optimal management policy. Numerical examples are provided

Perceptionization of FM/FD/1 queuing model under various fuzzy numbers

We present a FM/FD/1 queuing model with unbounded limit under different fuzzy numbers. The arrival (landing) rate and service (administration) rate are thought to be fuzzy numbers such as triangular, trapezoidal and pentagonal fuzzy numbers. Because random event can only be observed in an uncertain manner, the fuzzy result of an uncertainty mapping is a fuzzy random variable. Consequently, it is conceivable to characterize the specific connection between randomness and fuzziness. The execution proportions of this lining miniature are fuzzified after that examined by utilizing α-cut estimations and DSW algorithm (Dong, Shah and Wong). Relating to different fuzzy numbers, the numerical precedents are delineated to test the attainability of this model (miniature). A comparative illustration corresponding to each fuzzy number is accomplished for various estimations of α