This paper treats a discrete-time single-server finite-buffer exhaustive (singleand multiple-) vacation queueing system with discrete-time Markovian arrival process (D-MAP). The service and vacation times are generally distributed random variables and their durations are integral multiples of a slot duration. We obtain the queue-length distributions at departure, service completion, vacation te...

In this paper we introduce the adaptive MMAP[K] arrival process and analyze the adaptive MMAP[K]/PH[K]/1 queue. In such a queueing system, customers of K different types with Markovian inter-arrival times and possibly correlated customer types, are fed to a single server queue that makes use of r thresholds. Service times are phase-type and depend on the type of customer in service. Type k cust...

In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and one special skipping policy. Customers arrive in batches but are served by any order. The size of arriving batch becomes known upon its arrival at time instant total number customers is also known. According to adopted policy if batch, which greater than current system, arrives, all currentl...

Motivated by large-scale service systems with network structure and non-exponential customer abandonment, in a previous paper we introduced a non-Markovian time-varying open network of many-server fluid queues with customer abandonment from each queue and timevarying proportional routing among the queues, and showed how performance functions can be determined. The deterministic fluid model serv...

Primary motivation for this research is the need for firmly based but also easily computable methods applicable to the study of stability of stochastic models arising in lhe analysis of computer and communication systems. The stability definition adopted in this work is broad enough to cover such problems as existence of stationary distribution, ergodicity and nonergodi-city, finiteness of some...

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of processes, model not Markovian. In certain special circumstances, it Markovian generator if exciting function an exponential or sum fun...

This paper presents a novel methodology for approximating the queue length (the number of customers in the system) distributions of time-varying non-Markovian manyserver queues (e.g., Gt/Gt/nt queues), where the number of servers (nt) is large. Our methodology consists of two steps. The first step uses phase-type distributions to approximate the general inter-arrival and service times, thus gen...

In this paper, we consider two single server queueing systems to which customers of distinct priorities (P1 and P2) arrive according a Marked Markovian arrival process (MMAP). They are served phase type distributions. The probability P1 customer feedback is θ on completion his service. (P1) customers, as well P2 join the low priority queue. Low (P2) taken for service from head line whenever que...

The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the wor...