M θ/G/1/m and M θ/G/1 systems with the service time dependent on the queue length

The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

“…Reasoning as in the paper [4], from (11) we obtain formulas for the stationary distribution of the number of customers in the system. …”

“…In the general case, the essence of this strategy is that the service time distribution depends on the number of customers in the system at the beginning of each customer service [4]. With the help of the potentials method, we have developed an efficient algorithm for computing the stationary distribution of the number of customers in the systems with threshold functioning strategies [4][5][6][7][8].…”

Simulation-Based Optimization for the Operation of Toll Plaza at Car Park Exit with Mixed Types of Tollbooths and Waiting-Time-Dependent Service

“…Analytical modeling is based on the queueing theory, which uses known probability distributions to describe the cars' interarrival and tollbooths' service patterns. A large body of literature studies exists on the queueing system with dependent services, which are related to arrival rate [12], waiting time [13], queue length [14,15], or workload [16,17]. Nevertheless, the queueing theory fails when the probability distribution of either cars' interarrival or tollbooths' service is not all mathematically explicit or when the car's arrival rate is greater than the processing capacity in which the queue tends to be infinite.…”

The busy period for the MΘ/G/1/m system with service time dependent of the queue length

“…Continuing the research started in [1,2], in this paper we study the characteristics of the busy period of the system in which the service time of each customer is determined according to the rule: if at the moment of a customer service start there are n customers in the system, the distribution function of the customer service time is ( ).…”